The expressiοn that tells the weight οf the flοur left in the bag is 2 - 0.25
What is an expressiοn?A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expression or mathematical expression. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression.
Here, we have
Given: From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread.
We have to find the expression that tells the weight of the flour left in the bag.
Marcella took 1/4 pound to bake bread = 0.25
If Marcella took 0.25 pounds from a 2-pound flour bag then she left with 1.75 pounds.
Hence, the expression that tells the weight of the flour left in the bag is 2 - 0.25
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ngozi is twice as old as Ada and Agnes 13 1/3 of ada if sum of their age is 30 how old is ngozi
The age of Ngozi if ngozi is twice as old as Ada and Agnes 13 1/3 of ada if sum of their age is 30 is 3.68 years.
How old is Ngozi?Let
Ada age = x
Agnes age = 13 1/3x
Ngozi age = 2x
30 = x + 13 1/3x + 2x
30 = 3x + 40/3x
30 = 49/3x
divide both sides by 49/3
x = 30 ÷ 49/3
multiply by the reciprocal of 49/3
x = 30 × 3/49
x = 1.84 years
Ngozi age = 2x
= 2(1.84)
= 3.68 years
Therefore, Ngozi is 3.68 years old
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Which expression does not have the same value as −2+3×65 ?
The expression that does not have the same value as -2 + 3×65 is 3×(65-2) which evaluates to 183, the correct option is D.
The expression -2 + 3×65 represents a mathematical calculation that involves the operations of addition and multiplication. The order of operations dictates that multiplication should be done before addition, so we start by multiplying 3 and 65 and then adding the result to -2.
The value of -2 + 3×65 is 193.
we need to evaluate each expression and compare it to 193.
Option A: 3×65 - 2 = 193
Option B: (3-2)×65 = 65
Option C: 65×3 - 2 = 193
Option D: 3×(65-2) = 183
expression that does not have the same value as -2 + 3×65 is option D: 3×(65-2) which evaluates to 183.
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The complete question is :
Which expression does not have the same value as −2+3×65?
Option A: 3×65 - 2 = 193
Option B: (3-2)×65 = 65
Option C: 65×3 - 2 = 193
Option D: 3×(65-2) = 183
8. Effect size - Cohen's d and r squared An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist’s findings is that one year after the workshop, a sample of 49 job seekers who received training on setting career goals scored an average of 6.5 as measured on a 9-point job-search satisfaction scale, with a standard deviation of 1.2. The typical job seeker scores 5.8 points. The psychologist finds that the estimated Cohen’s d is , the t statistic is 4.12, and r² is . Using Cohen’s d and Cohen’s guidelines for interpreting the effect size with the estimated Cohen’s d, there is a treatment effect. Using r² and the extension of Cohen’s guidelines for interpreting the effect size using r², there is a treatment effect. (Hint: When using Cohen’s guidelines for interpreting the effect size, if the value lies between two categories, then specify the range covered by both categories, for example, medium to large.) Another one of the psychologist’s findings is that a sample of 144 job seekers who received training on identifying marketable skills worked more than 30 hours an average of 6.9 months in the last year, with a standard deviation of 2.5. The typical job seeker works 6.4 months. She finds that the estimated Cohen’s d is , the t statistic is 2.38, and r² is . Using Cohen’s d and Cohen’s guidelines for interpreting the effect size with the estimated Cohen’s d, there is a treatment effect. Using r² and the extension of Cohen’s guidelines for interpreting the effect size with r², there is a treatment effect.
For the first finding on job-search satisfaction scale, the estimated Cohen’s d is not provided in the question. However, assuming that it is provided in the actual data, the psychologist can use Cohen’s guidelines for interpreting the effect size based on the estimated Cohen’s d. According to Cohen’s guidelines, an effect size of 0.2 is considered small, 0.5 is considered medium, and 0.8 or higher is considered large. Therefore, the psychologist needs to compare the estimated Cohen’s d with these values to evaluate the effect size.
For the second finding on the number of months worked in the last year, the estimated Cohen’s d is also not provided in the question. The psychologist can use the same approach to evaluate the effect size using Cohen’s guidelines based on the estimated Cohen’s d.
Alternatively, the psychologist can also use r² as a measure of effect size. R² represents the proportion of variance in the outcome variable that is explained by the treatment or intervention. According to Cohen’s guidelines for r², an effect size of 0.01 is considered small, 0.09 is considered medium, and 0.25 or higher is considered large. Therefore, the psychologist can compare the estimated r² with these values to evaluate the effect size.
Based on the information provided, both findings show statistically significant results with treatment effects. However, the actual effect sizes cannot be evaluated without the estimated Cohen’s d or r² values.
Effect size for job-search satisfaction is Cohen's d = 0.7, t statistic = 4.12 and r² = 0.49.
According to Cohen's guidelines, a Cohen's d of 0.7 is considered a large effect size. This means that the workshop had a significant impact on the job-search satisfaction of the participants. The t statistic of 4.12 is also significant, indicating that the difference between the workshop participants and the control group is unlikely to have occurred by chance. The r² of 0.49 indicates that the workshop accounted for 49% of the variance in job-search satisfaction.
Effect size for months worked
Cohen's d = 0.36
t statistic = 2.38
r² = 0.13
According to Cohen's guidelines, a Cohen's d of 0.36 is considered a medium effect size. This means that the workshop had a significant impact on the number of months worked by the participants. The t statistic of 2.38 is also significant, indicating that the difference between the workshop participants and the control group is unlikely to have occurred by chance. The r² of 0.13 indicates that the workshop accounted for 13% of the variance in months worked.
Interpretation
Both of the effect sizes found by the psychologist are significant, indicating that the workshops had a positive impact on the job-search satisfaction and the number of months worked by the participants. The effect size for job-search satisfaction is larger than the effect size for months worked, suggesting that the workshop had a greater impact on job-search satisfaction than on the number of months worked.
Conclusion
The psychologist's findings suggest that the workshops had a positive impact on the job-search satisfaction and the number of months worked by the participants. The effect sizes for both outcomes are significant, and the effect size for job-search satisfaction is larger than the effect size for months worked. These findings suggest that the workshops may be an effective way to help unemployed people find jobs.
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Please help ASPA
Graph the functions on the same coordinate axis.
f(x)=-2x+1
g(x)=x²-2x-3
What are the solutions to the system of equations?
Select each correct answer.
(-2, -3)
(-2,5)
(2, -3)
(2,5)
(2, 3)
Answer: (2,-3) and (-2,5)
Step-by-step explanation:
Let us graph the two equations one by one.
If we compare this equation with the slope intercept form of a line which is given as we see that m = -1 and c =1
Hence the slope of the line is -2 and the y intercept is 1.
Hence one point through which it is passing is (0,1) .
Let us find another point by putting x = 1 and solving it for y Let us find another point by putting x = 2 and solving it for y Hence the another point will be (2,-3)Let us find another point by putting x = -2 and solving it for y Hence the another point will be (-2,5)Now we have two points (0,1) ,(1,-1) , (2,-3) and (-2,5) we joint them on line to obtain our line 2.
It represents the parabola opening upward with vertices (1,-4)Let us mark few coordinates so that we may graph the parabola.i) x=0 ; ; (0,-3)ii)x=-1 ; ; (-1,0)iii) x=2 ; ;(2,-3)iii) x=1 ; ;(1,-4)iii) x=-2 ; ;(-2,5)Now we plot them on coordinate axis and line them to form our parabolaWhen we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs.
A school has 500 students. The principal is to pick 30 students at random from the school to go to the Rose Bowl. How can this be done using a random-number table?
The way the principal can use a random - number table to pick 30 students from the school is explained below.
How to use a random number table ?To use a random-number table to select 30 students at random from a school of 500 students, the principal should :
Assign a unique number from 1 to 500 to each student in the school.Choose a starting point on the random-number table and begin reading the digits in pairs from left to right.Ignore any pairs that are outside the range of 01 to 50 (since there are 50 students per page).Whenever the principal encounters a pair of digits that falls within the range of 01 to 50, record the corresponding student number.Repeat steps 3 and 4 until you have recorded 30 student numbers.Check that there are no duplicates in the list of selected students.This method ensures that every student has an equal chance of being selected.
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A scientist compares the weights of strawberries from two different groups. The difference between the means of the weights for the two different groups is –10 grams. The scientist uses simulations to create a randomization distribution to try to determine the likelihood that the results happened by chance. The histogram represents the results of the 1,000 trials from the simulations.
Histogram. differences in means from random grouping.
According to the randomization distribution, is the difference in means due to chance or the group from which the measurements were made? Explain your reasoning.
Type your response in the space below.
A botanist is studying the research question, “Do seeds from a common plant take longer to germinate at 72 degrees Fahrenheit or at 75 degrees Fahrenheit?” They design an experiment in which they select 20 seeds and assign those seeds to 2 groups of 10 seeds each at random. The seeds in the first group are placed in an environment that is held at a constant temperature of 72 degrees Fahrenheit, and the seeds in the second group are placed in an environment that is held at a constant temperature of 75 degrees Fahrenheit. The germination times, in days, for each group are displayed in the table.
group 1 days to germinate group 2 days to germinate
14 14
14 13
14 14
13 14
13 13
14 13
15 14
14 14
14 15
15 13
The mean germination time for group 1 is 14 days, and the mean germination time for group 2 is 13.7 days.
a. How could the botanist get a randomization distribution to compare the two groups?
Type your response in the space below.
b. How would the botanist use the randomization distribution to determine whether the difference between the mean germination time for group 1 and the mean germination time for group 2 is due to chance?
Type your response in the space below.
Noah rolls a standard number cube 10 times and adds the values to get a sum of 28. Is that unusually low? Clare simulates rolling the number cube 10 times on a computer and adds the values. She repeats that process 100 times and creates a histogram of the results.
Histogram from 22 to 48 by 2’s. Sum of 10 rolls. Height of each bar is 1, 3, 4, 9, 9, 11, 16, 14, 12, 10, 5, 5, 1.
a. Based on the histogram, does 28 seem unusually low?
Select the correct choice.
A YesYes
B NoNo
Explain your reasoning.
Type your response in the space below.
b. The mean of Clare’s simulations is a sum of 35, and the standard deviation is 5.72. Using a normal distribution as an approximation of this distribution, what is the probability that a person would roll a sum less than 28? Round your answer to the nearest hundredth.
Type your answer in the box below.
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Answer: According to the histogram, a sum of 28 is not unusually low. The bar representing a sum of 28 has a height of 9, which is relatively high compared to some of the other bars. Additionally, the histogram is roughly symmetric, so a sum of 28 is not far from the mean of the distribution.
To find the probability that a person would roll a sum less than 28, we can standardize the value using the formula z = (x - mu) / sigma, where x is the sum of 28, mu is the mean of 35, and sigma is the standard deviation of 5.72.
z = (28 - 35) / 5.72 = -1.22
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than -1.22 is approximately 0.1112, or 11.12%. Therefore, there is about an 11.12% chance that a person would roll a sum less than 28.
Step-by-step explanation:
You are conducting a study testing whether depression symptoms are lower after participating in therapy compared to before. Given this information, complete the hypotheses in symbols:
Given this information, the complete hypotheses in symbols for the study is:
H0:μ_Post-μ_pre ≥ 0H0:μ_Post-μ_pre < 0What are the hypotheses symbol?In statistics, the null hypothesis is usually represented by the letter H with the subscript '0' (zero), as in H0. It's spelled H-null, H-zero, or H-nought. Simultaneously, the alternative hypothesis expresses the observations caused by the non-random cause. It is represented by the letters H1 or Ha.
The null and alternative hypotheses in symbols would be:
H0: μafter ≤ μbeforeHa: μafter < μbeforeNote: Where: H0 = null hypothesis, Ha = alternative hypothesis, μafter = population mean of depression symptoms after therapy and μbefore = population mean of depression symptoms before therapy
The null hypothesis states that the mean depression symptoms after therapy is less than or equal to the mean depression symptoms before therapy. The alternative hypothesis states that the mean depression symptoms after therapy is less than the mean depression symptoms before therapy.
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Find the length of QS
Answer:
112
Step-by-step explanation:
you have to find the length of QT and ST, then QS will be the hypotenuse (opposite of the right angle) of the triangle QTS.
use the formula:
c²=a²+b²
a²=c²-b²
1. to find QT:
QT²=53²-45²
QT²=2,809-2,025
QT²=784
QT=28
2.to find ST:
ST²=117²-45²
ST²=13,689-2,025
ST²=11,664
ST=108
3. find QS:
QS²=28²+108²
QS²=784+11,664
QS²=12,448
QS=111.570605
QS≈112
Help me! I need help with my homewor!
Answer:
Area of shaded region= 1142.96mm²
Step-by-step explanation:
•First calculate the Area covered by the interior circle.
•To calculate the Area of the exterior circle first add the two radii to get the radius from the centre of the interior circle to the circumference of the exterior circle.
•Use the calculated radius to calculate the Area covered from the centre to the circumference of the exterior circle.
•Now subtract the Area of the interior circle from the area covered by the bigger circle to get the Area of the shaded region.
Answer:
1141.76
Step-by-step explanation:
To solve for the area of the entire circle, we must first solve for the radius. Adding 6 and 14 will get us the total radius of the circle.
6 + 14 = 20Therefore, the radius of the entire circle is 20.
The expression you can use to solve for the area of a circle is:
Area = π × radius²Inserting the radius into the expression:
Area = π × 20²Therefore, the area of the entire circle is 400π.
If there is a hole in the circle in the shape of a circle, we must subtract the area of that hole to find the area of the shaded region.
Inserting 6 into the expression to solve for area:
Area = π × 6²Therefore, the area of the hole is 36π.
Now, we need to subtract the area of the gap from the area of the entire circle.
400π - 36π = 364πBecause π is approximately equal to 3.14, we can calculate an approximate value for 364π by multiplying 364 by 3.14. This gives us:
364 × 3.14 = 1141.76.Therefore, the area of the shaded region is [tex]1141.76^{2}[/tex]
Jayden throws a ball up in the air. The graph below shows the height of the ball h in feet after t seconds. Find the interval for which the ball's height is increasing.
The intervals during which the ball's height is increasing are: [0, 2.5] and
[5, 7.5]
What is an intervals?In a graph, an interval represents a range of values along the x-axis or y-axis. It is a continuous segment of the axis between two points, often used to indicate a particular range of values or a specific time period.
Since the graph represents the height of the ball h in feet after t seconds, we can find the interval during which the ball's height is increasing by examining the slope of the graph.
If the slope of the graph is positive, the height of the ball is increasing. If the slope is negative, the height of the ball is decreasing.
Looking at the graph, we can see that the slope of the graph is positive between approximately 0 and 2.5 seconds, and between approximately 5 and 7.5 seconds.
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I will mark you brainiest!
In completing the following proof, which of the following statements should be included?
Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC
A) CCPTC
B) CPCTC
C) CSATC
D) CASTC
Answer:
B) CPCTC (stands for Corresponding Parts of Congruent Triangles are Congruent) should be included in the proof. This statement is necessary to show that ΔDBE ≅ ΔFCE, which then allows us to conclude that DB ≅ FC.
Step-by-step explanation:
y=2/5+2 how to get the x intercept
Answer:
Step-by-step explanation:
The equation you provided, y = 2/5 + 2, appears to be missing the variable x. Assuming you meant y = 2/5x + 2, here's how you can find the x-intercept:
To find the x-intercept, we need to find the value of x when y = 0. This is because the x-intercept is the point on the graph where the line crosses the x-axis, and at that point, the y-coordinate is always 0.
So, we can set y = 0 in the equation:
0 = 2/5x + 2
Subtracting 2 from both sides:
-2 = 2/5x
Multiplying both sides by 5/2:
-5/2 = x
Therefore, the x-intercept is at the point (-5/2, 0).
x/15 = h make x the subject
Answer:
To make "x" the subject of the equation, we can isolate it on one side of the equation by multiplying both sides by 15:
x/15 = h
Multiplying both sides by 15 gives:
x = 15h
The equation in terms of "x" is x = 15h.
Step-by-step explanation:
fill in the sentence below with the description that most specially applies to the quadrilateral below
The quadrilateral is most specifically a parallelogram because the opposite sides are parallel to each other
What is a parallelogram?
A parallelogram is a geometric shape with four sides, where opposite sides are parallel and congruent (having the same length), and opposite angles are also congruent (having the same measure).
In other words, a parallelogram is a quadrilateral (a polygon with four sides) where both pairs of opposite sides are parallel.
The opposite sides of a parallelogram are equal in length, and its diagonals bisect each other. The area of a parallelogram is equal to the product of its base (one of its sides) and its height (the perpendicular distance between the base and the opposite side).
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Critical Thinking Question (5 pts.)
(You may use the back of the page to write your answer if needed). Here is a case-study for you to solve. Use what you learned
about blood types and Rhesus factor to solve this situation.
Two friends, Mike and Jake were returning late at night from a club in the same car. Suddenly, Mike, who was driving, lost control of
the car and they crashed into a big tree. Mike ended up with only a few bruises and scratches, but Jake got hurt.
Jake had internal bleeding and was taken to a hospital, but he lost a lot of blood and needed a blood transfusion. Mike, feeling
responsible for his friend's condition, wanted to donate blood to his friend. Both Mike and Jake had blood type O. So, in the ER, Mike
gave 2 pints of blood to Jake.
Two weeks later, Jake became anemic. So, Mike, being a good friend, decided to give blood again. However, after the second
transfusion, Jake went into an anaphylactic shock (severe immune response) and almost died.
What, do you think, was the problem here? Your answer should have two parts:
1. Explain, what happened in Jake's body after the first blood transfusion - why did he become anemic so soon after the transfusion?
(hint: it's not from bleeding)
2. Explain, what happened after the second blood transfusion - why did Jake go into an anaphylactic shock?
1.Jake became anemic after the first blood transfusion because his body reacted to the foreign antigens.
2.He went into an anaphylactic shock after the second transfusion due to an even stronger allergic reaction.
1. After the first blood transfusion, Jake became anemic because he was given type O blood, which is not compatible with his own blood type. Incompatible blood transfusions occur when a person is given blood that carries a different antigen than the one they have. In this case, Jake was given type O blood, which carries both the A and B antigens, while Jake’s own blood carries the Rh antigen. Therefore, Jake’s body reacted to the foreign antigens and created antibodies to fight against them. This reaction caused Jake to become equation anemic, as his body was not able to absorb the oxygen from the transfused blood.
2. After the second blood transfusion, Jake went into an anaphylactic shock because he was given type O blood, which carries both the A and B antigens, while Jake’s own blood carries the Rh antigen. Since Jake’s body had already created antibodies to fight against the foreign antigens, when it was exposed to the same foreign antigens a second time, his body reacted with an even stronger immune response. This reaction caused Jake to go into an anaphylactic shock. In other words, the second transfusion caused an allergic reaction in Jake’s body, which was much more severe than the allergic reaction caused by the first transfusion.
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What are the coordinates of the point that is of the way from G to F?
OA. (3,2)
OB. (5,-2)
O C. (1.5, 3)
OD. (4.5, -3)
4
6
2
-6 -4-2 0
ON
-2
-4
-6
Ty
F
2
4
6
G
X
The coordinates of the point that is halfway between G (2,4) and F (6,-6) is (4, -2).
What is coordinate?Coordinate is a pair of numbers that represents a position on a two-dimensional plane. Coordinates are usually written in the form (x, y), with the x-coordinate representing a position along the horizontal axis, and the y-coordinate representing a position along the vertical axis. Coordinates can also be used to represent positions on a three-dimensional plane in the form (x, y, z). These coordinates can be used to pinpoint a specific location or to describe the shape of a figure on a graph.
This can be calculated by taking the average of the x coordinates (2 + 6 = 8/2 = 4) and the average of the y coordinates (4 - 6 = -2/2 = -2).
Therefore, the point is (4, -2).
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Plot the following points and join them together and describe what you get, (1₁-1), (2,1), (3, 3), (4.5) (5.7)
Answer:
A positive line
Step-by-step explanation:
Answer:
Step-by-step explanation:
you get a straight line with a slope = 2
the line slants up and to the right
it passes through the y axis at the point (0, -3)
a retailer sold bat at 25% profit
Answer:
25% Profit = CP of 5 bats = 5x W
Step-by-step explanation:
If the 8th term of an A.P is twice the 4th term and the sum of the first terms is 47. find the five common difference
If the 8th term of an A.P is twice the 4th term and the sum of the first terms is 47. the five common difference is 3.
How to find the five common difference?Let the first term be "a" and the common difference be "d".
The 4th term of the AP is: a + 3d
The 8th term of the AP is: a + 7d
We know that the 8th term is twice the 4th term, so:
a + 7d = 2(a + 3d)
Simplifying and solving for "a", we get:
a = d
Substituting this value of "a" in the sum of the first terms, we get:
47 = (5/2)(2a + 4d)
47 = 5(a + 2d)
9.4 = a + 2d
Substituting the value of "a" from above, we get:
9.4 = 3d
d = 3.13333
d = 3 (approximately )
Therefore, the common difference (d) is approximately 3.
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Solve the system of equations using substitution. y = 4x y = 8x + 8 (−3, −12) (−2, −8) (2, 8) (3, 12)
Answer:
(- 2, - 8 )
Step-by-step explanation:
y = 4x → (1)
y = 8x + 8 → (2)
substitute y = 8x + 8 into (1)
8x + 8 = 4x ( subtract 4x from both sides )
4x + 8 = 0 ( subtract 8 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
substitute x = - 2 into (1)
y = 4x = 4(- 2) = - 8
solution is (- 2, - 8 )
Answer:(-2,-8)
Step-by-step explanation:
if you use a graph and find where they intercept that will give you the answer use desmos graphing
The table below shows Zoey's earnings on the job.
Time (hours)
Time (hours)
Earnings (dollars)
Earnings (dollars)
3
3
$
86.10
$86.10
11
11
$
315.70
$315.70
24
24
$
688.80
$688.80
What is the constant of proportionality between earnings and time in hours?
Answer: 11 and more
Step-by-step explanation:
This table shows the amount of money that Bradford saved in his savings account after different amounts of time.
Number of Months 4 8 18
Amount Saved ($) 50 100 225
What is the constant of proportionality?
Responses
0.08
0.08
12.5
12.5
25
25
50
Answer:
Number of Months 4 8 18
Amount Saved ($) 50 100 225
What is the constant of proportionality?
The constant of proportionality is 25.
Step-by-step explanation:
1, a 36 foot tree cast an 18 foot Shadow at the
Same time that a mail box carts a 4 foot shadow
how tall is the mail box
Answer:
We can use the concept of proportions to solve this problem. We know that the ratio of the height of the tree to the length of its shadow is the same as the ratio of the height of the mailbox to the length of its shadow.
Let's call the height of the mailbox "x". Then, we can set up the proportion:
height of tree / length of tree's shadow = height of mailbox / length of mailbox's shadow
Plugging in the values we know, we get:
36 / 18 = x / 4
Simplifying the left side of the equation, we get:
2 = x / 4
To solve for x, we can multiply both sides of the equation by 4:
8 = x
Therefore, the mailbox is 8 feet tall.
Step-by-step explanation:
Answer:
Height of mail box = 8 ft
Step-by-step explanation:
Given information,
→ 18 ft shadow is formed by a 36 ft tree.
→ A mail box casts 4 foot shadow.
Now we have to,
→ Find the height of the mail box.
Let us assume that,
→ Height of mail box = h
Forming the equation,
→ 36/18 = h/4
Then the value of h will be,
→ 36/18 = h/4
→ h/4 = 36/18
→ h/4 = 2
→ h = 2 × 4
→ [ h = 8 ft ]
Hence, the value of h is 8.
I need help with this IXL special right triangles
Answer:
Step-by-step explanation:
m = 30
10√3 · √3 = 10·3 = 30
Use the image to determine the line of reflection. Graph of polygon ABCDE with point E at negative 3 comma 1. A second polygon A prime B prime C prime D prime E prime with E prime at negative 3 comma negative 3. Reflection across the x-axis Reflection across the y-axis Reflection across y = −1 Reflection across x = −3
The line of reflection is y = -1, which is the equation of the horizontal line passing through the midpoint of the line segment joining E and E'.
A line section is what?Two different points on a line define the boundaries of a line segment in geometry. Or, a line segment is a section of the line that links two points, as another alternative. In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are set or identifiable.
According to the given information:From the given image, we can see that the original polygon ABCDE has point E at (-3, 1), and the reflected polygon A'B'C'D'E' has point E' at (-3, -3). This means that the reflection must have occurred across the horizontal line passing through the point (-3, -1), which is the midpoint of the line segment joining E and E'.
Therefore, the line of reflection is y = -1, which is the equation of the horizontal line passing through the midpoint of the line segment joining E and E'.
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Question 1 1.1. Express each of the ratios below in the simplest form. Show all you steps and calculations. 1.1.1. 75: 125 1.1.2. 3mm: 3m 1.1.3. 7500g: 2 Kg 1.1.4.250ml: 21 1.1.5. 250 kg: 2 tonnes bank fo
The ratio of 75:125 is 3:5.
The ratio 3 mm : 3000 mm is 1:1000.
The ratio of 7500g:2 Kg is 3.75:1.
The ratio of 250ml:2l is 1:8.
How to calculate the ratioTo simplify this ratio, we need to find the greatest common factor (GCF) of 75 and 125, and divide both terms by it.
The factors of 75 are: 1, 3, 5, 15, 25, 75.
The factors of 125 are: 1, 5, 25, 125.
The GCF is 25.
Dividing both terms by 25, we get:
75 ÷ 25 = 3
125 ÷ 25 = 5
Therefore, the simplified ratio is 3:5.
1.1.2. 3mm:3m
To simplify this ratio, we need to convert the units so that they are the same.
1 m = 1000 mm
So, 3 m = 3000 mm
Now, the ratio is 3 mm : 3000 mm.
We can simplify this ratio by dividing both terms by 3:
3 mm ÷ 3 = 1 mm
3000 mm ÷ 3 = 1000 mm
Therefore, the simplified ratio is 1:1000.
1.1.3. 7500g:2 Kg
To simplify this ratio, we need to convert either grams to kilograms or kilograms to grams so that both terms have the same unit.
7500 g = 7.5 kg (since 1 kg = 1000 g)
Now, the ratio is 7.5 kg : 2 kg.
We can simplify this ratio by dividing both terms by 2:
7.5 kg ÷ 2 = 3.75 kg
2 kg ÷ 2 = 1 kg
Therefore, the simplified ratio is 3.75:1.
1.1.4. 250ml:21
To simplify this ratio, we need to convert milliliters to a whole number.
We can convert 250 ml to 250/21 ml by dividing both terms by 21:
250 ml ÷ 21 = 11.9 ml (rounded to one decimal place)
Now, the ratio is 11.9 ml : 21.
We can simplify this ratio by dividing both terms by 0.1:
11.9 ml ÷ 0.1 = 119 ml
21 ÷ 0.1 = 210
Therefore, the simplified ratio is 119:210.
1.1.5. 250 kg:2 tonnes
To simplify this ratio, we need to convert either kilograms to tonnes or tonnes to kilograms so that both terms have the same unit.
1 tonne = 1000 kg
So, 2 tonnes = 2000 kg
Now, the ratio is 250 kg : 2000 kg.
We can simplify this ratio by dividing both terms by 250:
250 kg ÷ 250 = 1 kg
2000 kg ÷ 250 = 8 kg
Therefore, the simplified ratio is 1:8.
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QUESTION 1 The number of elements in sets A and B are shown in Figure 1.0. If n(A) = n(B) find: (a) x (b) n(A) (c) n(B) (d) n(AUB) 2x 4xx+5 Figure 1.0 10 marks
Answer:
From the given figure, we can write the following equations:
n(A) = 2x + 4
n(B) = x + 5
n(A∪B) = n(A) + n(B) - n(A∩B)
Since we are given that n(A) = n(B), we can substitute the expressions for n(A) and n(B) to get:
2x + 4 = x + 5
x = 1
(a) x = 1
(b) n(A) = 2x + 4 = 2(1) + 4 = 6
(c) n(B) = x + 5 = 1 + 5 = 6
(d) n(A∪B) = n(A) + n(B) - n(A∩B)
We still need to find n(A∩B) to calculate n(A∪B). Looking at the figure, we can see that there are 2 elements that are common to both A and B. Therefore,
n(A∩B) = 2
Substituting this value, we get:
n(A∪B) = n(A) + n(B) - n(A∩B) = 6 + 6 - 2 = 10
Therefore, (d) n(A∪B) = 10.
Step-by-step explanation:
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer chili on a hot dog?
900
2,000
2,100
4,000
Answer:
The answer to your problem is, A. 900
Step-by-step explanation:
How we would need to find it:
To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.
27/150 = 0.18
Next, estimate the number of people who prefer mustard in the entire population of 5,000 attendees we can multiply/x this proportion by the total number of attendees:
0.18 x 5,000 = 900
Thus the answer to your problem is, A. 900
state of each triangle is acute, obtuse, or right show work
The triangle can be classified as follow:
15: obtuse
16: right
How to know if a triangle is acute based on side lengths?To classify the triangle as acute, obtuse, or right, follow the following steps:
1. Calculate the sum of squares of the two smaller sides.
2. Compare it to the square of the longest side.
3. If the sum is greater, your triangle is acute. If they are equal, your triangle is right. If the sum is less, your triangle is obtuse.
No. 15
10² + (2√39)² = 256
18² = 324
256 < 324 (obtuse)
No. 16
11² + (2√19)² = 197
(√197)² = 197
197 = 197 (right)
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MATHEMATICS
1. If each interior angle of a regular polygon is five times the exterior angle, how many sides has the polygon? x° зх°6x° 4xº 4x° 2x⁰ 2. Find the value of X in the polygon drawn above.
1. The number of sides of the polygon is 8
2. The value of x is 36
What is a polygon?A polygon can be defined as a flat or plane. The sum of a regular polygon is expressed as (n-2)180. The sum of exterior angle of a polygon is 360.
Therefore the sum of the interior is 5 times the exterior.
(n-2)180 = 5×360
180n - 360 = 1800
180n = 1800-360
180n = 1440
divide both sides by 180
n = 1440/180
n = 8
therefore the number of sides of the polygon is 8
2. The number of sides of the polygon is 6
Therefore the sum of angle in the polygon = 6-2)180 = 4× 180
= 720°
x+3x+6x+4x+4x+2x = 720
20x = 720
x = 720/20
x = 36
therefore the value of x is 36
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