the combined mean and standard deviation for these exams will be Mean, 5. 66; standard deviation, 2. 055.
Combined mean=5.66
Combined standard deviation = 2.06
Combined mean= (MXa+ n×Xb)/(m+n)
Combined mean =2.80+2.86=5.66
Combined mean= sqrt(1.55)^2+(1.35)^2)
Combined deviation = 2.06
The mean is the number you get by separating the amount of a bunch of values by the quantity of values in the set.
Conversely, the middle is the center number in a bunch of values when those values are organized from littlest to biggest.
The mode of a bunch of values is the most often rehashed esteem in the set.
to know more about mean click here:
https://brainly.com/question/14532771
#SPJ4
Miller is going to install baseboard around the perimeter of her room's rectangular floor, shown below. The floor has dimensions 15 feet by 20 feet. The 2 doorways in her room are each 3 feet wide and do not require baseboard. Assuming an average cost of $0.30 per linear foot requiring baseboard, how much will it cost Naomi to purchase baseboard for her room? Use the CER strategy to explain your answer.
If Miller is going to install baseboard around the perimeter of her room's rectangular floor, s. it will cost Miller $19.20 to purchase baseboard for her room, assuming an average cost of $0.30 per linear foot requiring baseboard.
What is the cost price?To find out how much it will cost Miller to purchase baseboard for her room, we can use the CER (Conversion, Equation, and Re-substitution) strategy.
Conversion:
We can calculate the perimeter of the room by adding the lengths of all four sides:
Perimeter = 2(Length + Width) - 2(Doorway Width)
Perimeter = 2(15 + 20) - 2(3)
Perimeter = 64 feet
So, Miller will need 64 feet of baseboard.
Equation:
To calculate the cost of the baseboard, we can use the formula:
Cost = Length * Cost per linear foot
In this case, the length is 64 feet and the cost per linear foot is $0.30.
Cost = 64 * 0.30
Cost = $19.20
Therefore the final answer is that it will cost Miller $19.20 to purchase baseboard for her room, assuming an average cost of $0.30 per linear foot requiring baseboard.
Learn more about cost here:https://brainly.com/question/29509552
#SPJ1
Work out 2 and 1/2 x 1 and 4/5
Give your answer as a mixed number in its simplest form
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
You are flipping two coins. Find the probability of flipping two tails.
A. 1/2
B. 1/24
C. 1/8
D. 1/4
Answer:
D. 1/4
Step-by-step explanation:
The probability of flipping a tail is 1/2. To find the probability of flipping two tails, multiply.
1/2 x 1/2 = 1/4
Answer: Here we will learn how to find the probability of tossing two coins.
Let us take the experiment of tossing two coins simultaneously:
When we toss two coins simultaneously then the possible of outcomes are: (two heads) or (one head and one tail) or (two tails) i.e., in short (H, H) or (H, T) or (T, T) respectively; where H is denoted for head and T is denoted for tail.
Therefore, total numbers of outcome are 22 = 4
The above explanation will help us to solve the problems on finding the probability of tossing two coins.
Step-by-step explanation:
THE ANSWER MUST BE AT LEAST 1/4 OR 1/8
IF THAT IS WRONG LET ME KNOW!
AND IF YOU NEED A TUTOR I AM OPEN FOR HELP JUST CONTACT ME IF YOU HAVE ANY QUESTIONS!
A car dealer has 20 Toyota Camrys and 25 Honda Accords left on the parking lot. The dealer wants to arrange the cars in rows so that each row has the same number of vehicles and the same number of vehicles of each type. What is the greatest number of rows that can be formed?
There will be __ rows with __ Toyota Camrys and __Honda Accords in each row.
Greg set a goal of raising enough money to buy a new bicycle that cost $210 he has already re-$60 and he will earn $15 for each long that he mows this summer which number line represents the number of lawns can mow and meet his goal?
Option 1 is correct, The point will be on 10 for the cost $240.
=> 0—————————-10—————————-20
An unitary methοd is what?By multiplying the data οbtained with such a nanοsectiοn variable whilst alsο twο that used the unitary methοd , the jοb can be finished. In essence, this mean that whenever a desired item appears, the specified entity is set οr the cοlοur space οf bοth prοductiοn runs is skipped. A varying fee οf Inr ($1.01) might have been necessary fοr fοrty pens.
Here,
Greg wants tο cοllect enοugh cash tο spend $210 οn a new bicycle. He needs tο make an extra $150 because he already has $60. He needs tο mοw the fοllοwing lawns in οrder tο make his $15 per lawn:
=> 150 ÷ 15 = 10 acres
Greg must mοw at least 10 yards in οrder tο accοmplish his οbjective. The number line shοwing hοw many fields he can mοw is as fοllοws:
=> 0—————————-10—————————-20
The number οf lawns he can mοw tο reach his οbjective is represented by any value οn this number line larger than οr equal tο 10. He will, fοr instance, be cοmpensated:
=> 12 × $15 = $180
He already has $60, sο after adding this, he will have:
=> $60 + $180 = $240
which will cοver the cοst οf the new mοtοrbike.
To know more about unitary method visit:
brainly.com/question/28276953
#SPJ1
What is the interest on a $1,000, 18-month loan, with a 10% simple interest rate?
Answer:
$150
Step-by-step explanation:
Interest = Principal x Rate x Time
where Principal is the amount borrowed, Rate is the interest rate, and Time is the duration of the loan.
In this case, the Principal is $1,000, the Rate is 10%, and the Time is 18 months (which we'll convert to a fraction of a year).
First, we need to convert 18 months to a fraction of a year. Since there are 12 months in a year, 18 months is equal to 18/12 = 1.5 years.
Using the formula:
Interest = Principal x Rate x Time
Interest = $1,000 x 0.10 x 1.5
Interest = $150
So the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.
Answer:
The formula for simple interest is I = Prt, where I is the interest, P is the principal or amount borrowed, r is the interest rate, and t is the time in years.
In this case, P = $1,000, r = 10% or 0.10 as a decimal, and t = 1.5 years (since 18 months is equivalent to 1.5 years).
I = Prt
I = $1,000 * 0.10 * 1.5
I = $150
Therefore, the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.
On her math homework, Emely got 13 questions correct for every 7 questions she got wrong. What percentage of her math homework questions did Emely get wrong?
Emely gοt 35% οf her math hοmewοrk questiοns wrοng.
What is the percentage?A percentage that represents a tenth οf a quantity. One percent, denοted by the symbοl 1%, is equal tο οne-hundredth οf sοmething; hence, 100 percent denοtes the full thing, and 200 percent designates twice the amοunt specified. A pοrtiοn per hundred is what the percentage denοtes. The percentage refers tο οne in a hundred. The % sign is used tο denοte it.
Emely gοt 13 questiοns cοrrect fοr every 7 questiοns she gοt wrοng.
We can start by finding the fractiοn οf questiοns Emely gοt wrοng, which is 7/(7+13) = 7/20. Tο cοnvert this tο a percentage, we can multiply by 100 tο get 35%.
Therefore, Emely got 35% of her math homework questions wrong.
Learn more about percentages, by the following link.
https://brainly.com/question/24304697
#SPJ1
What is equivalent to the answer in
8(2y+1/4)?
FYI the “1/4” is not divided it’s a fraction
Answer:
[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find an \underline{equivalent expression}.}[/tex]
[tex]\textsf{This expression is set up to allow us to use the \underline{Distributive Property}.}[/tex]
[tex]\Large\textsf{What is the Distributive Property?}[/tex]
[tex]\textsf{The \underline{Distributive Property} is a property that allows us to distribute.}[/tex]
[tex]\large\underline{\textsf{For this problem;}}[/tex]
[tex]\textsf{We can use the Distributive Property to distribute the 8 into values in the Parentheses.}[/tex]
[tex]\large\underline{\textsf{Distribute:}}[/tex]
[tex]\mathtt{8(2y+\frac{1}{4} )}[/tex]
[tex]\mathtt{(8 \times 2y) + (8 \times \frac{1}{4}) .}[/tex]
[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]
Answer:
16y + 2
Step-by-step explanation:
Now we have to,
→ Find the equivalent expression.
The expression is,
→ 8(2y + (1/4))
Let's simplify the expression,
→ 8(2y + (1/4))
→ 8(2y) + 8(1/4)
→ 16y + (8/4)
→ 16y + 2
Hence, the answer is 16y + 2.
Which value of x is the solution to this equation? 5x2 = 30x – 45
Answer:
x = 11/6 or 1 5/6 or 1.83333...
Step-by-step explanation:
The solution to the equation 5x^2 = 30x – 45 is x = 3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have the Equation: 5x² = 30x - 45.
We can start by simplifying the equation by subtracting 30x and adding 45 from both sides to get:
5x² - 30x + 45 = 0
We can further simplify by dividing both sides by 5 to get:
x² - 6x + 9 = 0
This can be factored as (x - 3)(x - 3) = 0, which means that the only solution is x = 3.
Therefore, the solution to the equation 5x^2 = 30x – 45 is x = 3.
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ2
Suppose that a factory produces light bulbs, and the percentage of defective bulbs is 3.5% . If a sample of 550 light bulbs is selected at random what is the probability that the number of defective bulbs in the sample is greater than 15
probability-=0.3419
The probability that the number of defective bulbs in a sample of 550 light bulbs is greater than 15 is 0.3419. To calculate this probability, you need to use the binomial probability formula: P(x) = nCx * p^x * q^(n-x), where n is the sample size (550), p is the probability of a defective bulb (0.035), x is the number of defective bulbs you want to calculate (15) and q is the probability of a non-defective bulb (1-0.035). Plugging in the values, we get P(x) = 550C15 * 0.035^15 * 0.965^(550-15) = 0.3419
Learn more about probability
brainly.com/question/29381779
#SPJ4
A bag contains marbles 3 red, 4 green, and 5 white. If a marble is pulled from the bag what is the probability it will be green
If a bag contains 3 red, 4 green, and 5 white marbles, then the probability that a green marble will be selected in the first attempt is equal to 4/12 or 1/3.
Probability is defined as the likeliness of an event to happen. It simply means possibility of any event to occur or the possibility of an event to not occur. The sum of the possibilities in any event is always equal to one. In the given case, there are 3 red, 4 green, and 5 white marbles.
Now total number of marbles is equal to 3+4+5 = 12 marbles
Probability that the green marble is picked first = 4/12 = 1/3
Learn more about probability at:
brainly.com/question/13604758
#SPJ4
Please Show detailed algebraic work.
Using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
Given,
The initial amount of caffeine in the beverage = 120 mg
The rate at which the caffeine decreases = 12% per hour w
We are asked to find the time taken for the caffeine amount to become 10mg.
Now let the initial amount be 100 per cent.
After one hour, the amount becomes (100-12) = 88% of 120 = 0.88 * 120
So after every one hour, there is 88% caffeine left.
Now after two hours,
the amount of caffeine = 88% of (0.88*120) = 0.88*0.88*120 = 120(0.88)²
So after x hours, we can write the equation as:
Amount of caffeine left C(x) = 120(0.88)ˣ
Now for 10mg to be left, the time taken is:
10 = 120(0.88)ˣ
1/12 = (0.88)ˣ
log (1/12) = x log(0.88)
-1.079 = x (-0.056)
x = 19.27 hours
Therefore using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.
To learn more about the equations, follow the link.
brainly.com/question/22688504
#SPJ1
Problem #2 (15 Points)
2. A report by a tourism company says that 28% of United States citizens plan to travel
internationally annually. The tourism company selects a random sample of 40 people and
calculates the sample proportion (p) of people planning to travel internationally.
a. Tell whether n-p≥10 and n-(1 p)≥10 are true or false.
F +
+Show your work here:
-
b. Describe the shape of the sampling distribution of the sample proportion of people
who expect to travel internationally the next year. Write an explanation for your
reasoning.
Show your work here:
Answer:
Step-by-step explanation:
its b
Harry, Jason and Sarah are taking the GMAT which is required by most applicants for admission to graduate schools of business. The three friends want to get admissions to three different business schools. Harry can get the admission if he gets a score above 650 in GMAT, Jason can get the admission if he gets above 630 and Sarah can get the admission if she gets above 670. Scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115. What is the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another.
Probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.
The probability of Harry, Jason, and Sarah getting admission to their desired schools is the probability that Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670. The scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115.So, let's first standardize Harry's score:Z = (650 - 550) / 115 = 0.87Similarly, for Jason's score:Z = (630 - 550) / 115 = 0.70And for Sarah's score:Z = (670 - 550) / 115 = 1.04Now we need to find the probabilities of getting each of these Z-values. We can do that using the standard normal distribution table. The table gives the probability that a standard normal random variable is less than or equal to a certain Z-value.To find the probability that Harry's score is above 650, we need to find the probability that Z > 0.87. This can be found by subtracting the probability of Z ≤ 0.87 from 1:P(Z > 0.87) = 1 - P(Z ≤ 0.87) = 1 - 0.8078 = 0.1922Similarly, the probability that Jason's score is above 630 is:P(Z > 0.70) = 1 - P(Z ≤ 0.70) = 1 - 0.7580 = 0.2420And the probability that Sarah's score is above 670 is:P(Z > 1.04) = 1 - P(Z ≤ 1.04) = 1 - 0.8508 = 0.1492The probability that all three events occur (Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670) is the product of their probabilities:P(Harry, Jason, and Sarah) = P(Z > 0.87) × P(Z > 0.70) × P(Z > 1.04) = 0.1922 × 0.2420 × 0.1492 = 0.0088Therefore, the probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.
Learn more about Probability
brainly.com/question/15036999
#SPJ4
Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places. X y
2 8. 18
6. 5 12. 816
11 16. 768
15. 5 21. 222
20 26. 462
24. 5 31. 36
29 34. 584
y
=
x
+
The missing coefficients in the equation y = mx + b are m = 0.841 and b = 18.813. The final equation that fits the given data is y = 0.841x + 18.813
To find the missing coefficients in the equation y = mx + b, we need to use the given data in the table to determine the values of m and b.
We can start by using two of the data points to set up a system of equations:
Using (5, 23.018) and (6, 23.859):
m(5) + b = 23.018
m(6) + b = 23.859
Subtracting the first equation from the second equation gives:
m(6) - m(5) = 0.841
Simplifying this expression:
m = 0.841 / (6 - 5) = 0.841
Now we can substitute the value of m into one of the original equations to solve for b:
m(5) + b = 23.018
0.841(5) + b = 23.018
b = 23.018 - 4.205
b = 18.813
Therefore, the missing coefficients are:
m = 0.841
b = 18.813
The equation y = 0.841x + 18.813 fits the given data.
Learn more about coefficients here
brainly.com/question/28993561
#SPJ4
The given question is incomplete, the complete question is:
Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places. X y 5 23.018 5.5 23.438 6 23.859 6.5 24.035 7 25.449 7.5 24.868 8 26.058 I Enter an integer or decimal number [more..] y = I+
Determine the power consumed by the resistor
The power consumed by resistor R3 is 0.79 watts.
What is power?The rate at which energy is transferred or converted is known as Power. It is a measure of how much work can be done in a given amount of time. Power is typically measured in watts and is a key factor in determining the efficiency of machines and systems.
To determine the power consumed by resistor R3, we need to first find the current flowing through it.
E₁ = I(R₁ + R₂ + R3 + R4)
I = E₁ / (R₁ + R₂ + R3 + R4)
= 30 / (152 + 202 + 252 + 102)
= 0.056 A
Now that we know the current flowing through R3, we can use Ohm's Law again to find the power consumed by it:
P = I²R3
= (0.056)² x 252
= 0.79 W
To know more about Ohm's Law visit:
https://brainly.com/question/1247379
#SPJ1
Evaluate 1/3 · 5/6
GIVING 20 POINTS
what is the slope from (-4,6) to (2, 3/2)?
Answer:
1\2
Step-by-step explanation:
A hardware store charges a $40 rental fee and
$20 per day to rent a power washer. Which
equation correctly relates the total cost y to rent the
washer for x days? 8. F. 1-3
A. Y=20+40x. B. Y=40+20x
C. Y=40 -x/20.
D. Y=20 -x/ 40.
The equation correctly relates the total cost y to rent the washer for x days is option (B) Y = 40 + 20x
The rental fee of $40 is charged regardless of the number of days the power washer is rented. In addition to this fee, there is a daily charge of $20 per day.
Therefore, the total cost of renting the power washer for x days can be calculated by multiplying the daily charge by the number of days rented and adding the rental fee:
Total cost = (daily charge) x (number of days rented) + rental fee
Total cost = $20x + $40
This linear equation can be rearranged to the form:
Y = 40 + 20x
Therefore, the correct option is (B) Y = 40 + 20x
Learn more about linear equation here
brainly.com/question/13738061
#SPJ4
Can someone show me an example on how to solve a y=mx+b equation?
Answer:
hey, good afternoon!
Step-by-step explanation:
here is an example: the cost of a pizza is 7.50 and you can add a topping for 0.65 cents. find the cost of the pizza with 6 toppings
y=mx+b
the x stands for the toppings and y is the cost. the rate is 0.65 cents and the orginal amount of money is b. so the equation would look like this:
y= .65x+7.50. x=6
y = 65(6)+7.50
=3.9+ 7.50= $11.50(answer)
the m is the rate of change in this question is 0.65 cents
b is initial/ fixed/ value once again in this qeustion it 7.50$
hope this helps. have a great day!
Which research scenario would most likely be biased against non-voters? Select all that apply.
1. a convenience sample collected at a political rally used to determine candidate preferences
2. a volunteer sample collected at a political rally used to determine candidate preferences
3. a simple random sample of all non-voters used to determine why they don’t vote
4. a simple random sample of all eligible voters, some of whom didn’t have time to vote
5. a volunteer sample collected at large department store to determine who they voted for
The scenariο that wοuld mοst likely be biased against nοn-vοters is a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences
What is a biased expressiοn?A cοgnitive bias clοuds οur critical thinking and may result in the spread οf false infοrmatiοn that may be harmful tο οther peοple. Biases cause us tο avοid infοrmatiοn that might be uncοmfοrtable οr unwelcοme rather than lοοking intο the infοrmatiοn that might help us reach a mοre accurate cοnclusiοn.
A cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences is nοt a biased sample. Since the nοn-vοters are nοt
A vοlunteer sample cοllected at a pοlitical rally was used tο determine candidate preferences. It prefers a particular member. This is a biased survey.
A simple randοm sample οf all nοn-vοters was used tο determine why they dοn’t vοte. It is biased. Because a grοup οf peοple decides nοt tο give a vοte.
A simple randοm sample οf all eligible vοters, sοme οf whοm didn’t have time tο vοte. It is a sample.
A vοlunteer sample was cοllected at a large department stοre tο determine whο they vοted fοr. It is a nοn-biased survery. The peοple dο nοt prefer a particular team.
To learn more about sample,
https://brainly.com/question/1470144
#SPJ1
The area of this circle is 72π m².
What is the area of a 45º sector of this circle?
Responses
8π m²
9π m²
12π m²
18π m²
The area of the sector is evaluated to be equal to 9π square meters
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
For the area of circle 72π m²;
πr² = 72π m²
r² = 72 m²
hence the area of the sector is calculated as follows:
area of the sector = (45°/360°) × π × 72 m²
we simplify by multiplication and division
area of the sector = 1/8 × π × 72 m²
area of the sector = π × 9 m²
area of the sector = 9π m².
Therefore, the area of the sector is evaluated to be equal to 9π square meters
Know more about area of sector here: https://brainly.com/question/22972014
#SPJ1
What is the value x + y? (Round your answer to the nearest tenth)
Answer:
x + y = 110
Step-by-step explanation:
[tex]x=\sqrt{(65^{2} - 56^{2} } \\x=33\\\\\\y=\sqrt{(85^2-36^2} \\y=77\\\\x+y=33+77\\x+y=110[/tex]
Solve the following formula for t.
Q=F+ Frt
(Simplify your answer.)
Find the slope of the line that passes through the pair of points (7/20,5/19)and 5/9,11/16)
The slope of the line that passes through the pair of points (7/20,5/19) and (5/9,11/16) is 3/5.
To find the slope of a line passing through two points, we need to use the slope formula. The slope formula is m = (y2 - y1) / (x2 - x1). To calculate the slope, we need to first calculate the x and y values of the two points, (7/20,5/19) and (5/9,11/16). The x values are 7/20 and 5/9 and the y values are 5/19 and 11/16. We can then plug these values into the slope formula to get the slope. The slope is (11/16 - 5/19) / (5/9 - 7/20) = 3/5. Therefore, the slope of the line that passes through the two points (7/20,5/19) and (5/9,11/16) is 3/5.
Learn more about slope here
https://brainly.com/question/3605446
#SPJ4
What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or
leave in terms of π. Show your work.
As a result, the answer to the following question, As a result, the supplied radius arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).
what is radius?In more modern use, the length of a sphere or sphere is equal to its radius in standard geometric, so it has several line segments from its centre to its circumference. The phrase is derived from the Latin word for radius, which also referred to the spokes of a waggon wheel. The radius of a circle is the distance between the centre and any point on its periphery. Often, "R" or "r" is used to signify it. A radius is a boundary line with one terminus in the centre and a second around the perimeter of a circle. Vide letter diameter equals radius The dimension of a circle is the segment that passes its centre and has extremities that are on the circle.
The formula for calculating the arc length of a circle is:
Arc length = radius x central angle in radians,
In order to use this formula, we must first convert the centre angle from degrees to radians. We are aware of the following:
2 radians Equals 360 degrees
360 degrees divided by 2 radians equals x degrees divided by y radians
(x degrees * 2 radians) / 360 degrees = y
y = (22 deg * 2 radians) / 360 deg = 0.38397 deg (rounded to five decimal places)
arc length Equals radius multiplied by Centre angle in radians
With r = 18 inches and = 0.38397 radians, we get:
arc length = 18 inches multiplied by 0.38397 equals 6.9115 inches (rounded to four decimal places)
As a result, the supplied arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).
To know more about radius visit:
https://brainly.com/question/28946570
#SPJ1
answers for these please
The values of the variables are x = 2, z = 6.92, x = 10.5 and y = 12.6
How to find the values of the variablesFigure 12
In this figure, we make use of the following theorem of intersecting secants
AB * AC = AD * AE
By substitution, we have
(x + 4) * (x + 4 + x - 2) = 4 * 9
Evaluate the sum
(x + 4) * (2x + 2) = 36
So, we have
(x + 4) * (x + 1) = 18
Expand
x^2 + 5x + 4 = 18
Evaluate the like terms
x^2 + 5x - 14 = 0
Factorize
(x + 7)(x - 2) = 0
Solve for x
x = -7 or x = 2
x cannot be negative
So, we have
x = 2
Figure 13
In this figure, we make use of the following theorem of intersecting secant-tangent
XU * WU = UV^2
So, we have
8 * 6 = z^2
Evaluate
z^2 = 48
Take the square root
z = 6.92
Figure 14
Using the same theorem used in (13), we have
2 * (2 + x) = 5^2
So, we have
4 + 2x = 25
Evaluate
2x = 21
Divide
x = 10.5
Figure 15
Using the same theorem used above
y^2 = 8 * 20
So, we have
y^2 = 160
Take the square root
y = 12.6
Hence, the value of y is 12.6
Read more about secant and tangent lines at
https://brainly.com/question/16038958
#SPJ1
3. Consider the quadratic equation x2 + 2x - 35 = 0. Solve by factoring and using the zero-product property. What are solutions to quadratic equations called? Show your work.
To solve the equation, factor [tex]\bold{x^2+2x-35}[/tex] use the formula [tex]\bold{x^2 +(a + b) x + ab = (x + a)(x + b)}[/tex]. To find a and b, set up a system to be solved.
[tex]a + b = 2[/tex]
[tex]ab = -35[/tex]
Since ab is negative, a and b have opposite signs. Since [tex]a+b[/tex] is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.
[tex]\bold{-1.35}[/tex][tex]\bold{-5.7}[/tex]Calculate the sum of each pair.
[tex]\bold{-1 + 35 = 34}[/tex][tex]\bold{-5 + 7 = 2}[/tex]The solution is the pair that gives sum 2.
[tex]\bold{a = -5}[/tex][tex]\bold{b = 7}[/tex]Rewrite the factored expression [tex](x + a)(x + b)[/tex] with the values obtained.
[tex]\bold{(x -5)(x + 7)}[/tex]To find solutions to equations, solve [tex]x-5=0[/tex] and [tex]x+7=0[/tex].
[tex]\bold{x = 5}[/tex][tex]\bold{x = -7}[/tex]What are the solutions of quadratic equations called?The "solutions" of a Quadratic Equation are the values where the equation equals zero. They are also called "roots", or even "zeros".
To learn more about quadratic equations, I kindly invite to check this verified question: https://brainly.com/question/17165891
I am an integer in quadrant to my exponent is less than -1 my y-coordinate is more than two my x-coordinate is greater than -3 the sum of the absolute values of my coordinates is five who am I
The integer that satisfies all of these conditions is -4.
Exponentiating -4 gives 16, which is less than -1.
The y-coordinate of -4 on the coordinate plane is above 2.
The x-coordinate of -4 on the coordinate plane is greater than -3.
And, the sum of the absolute values of the coordinates of -4 is 7, which is equal to five.
What conclusion can be determined by the dot plot
Dot plots are useful for visualizing the distribution of data and identifying patterns, trends, and outliers. They are often used in data analysis, quality control, and scientific research to help draw conclusions and make informed decisions based on data.
A dot plot is a graphical representation of statistics that presents character information factors through the use of dots. From a dot plot, possible decide several conclusions, depending on the data being displayed.
For instance, if the dot plot presents information on the height of a collection of people, you can still determine the range of heights inside the organization, the most common top, and any outliers (i.e., individuals with severe heights).
If the dot plot displays facts at the ratings of a collection of students on a test, you can still determine the range of rankings, the median score, and the distribution of rankings (i.e., whether or not the ratings are evenly distributed or clustered round sure values).
Learn more about the dot plot:
brainly.com/question/21862696
The complete question is:
What conclusion can be determined by the dot plot? Explain in detail about the dot plot.
#SPJ4