9514 1404 393
Answer:
smaller: -4larger: -1Step-by-step explanation:
Substituting the given variables into the word problem, we have two equations:
3x +3y = -15
6x -3y = -21
Adding these equations eliminates y:
9x = -36
x = -4 . . . . divide by 9
Using this in the first equation, we have ...
3(-4) +3y = -15
-4 +y = -5 . . . . . divide by 3
y = -1 . . . . . . . . . add 4
The smaller number is -4; the larger is -1.
A regional office of the Internal Revenue Service randomly distributes returns to be audited to the pool of auditors. Over the thousands of returns audited last year, the average amount of extra taxes collected was $356 per audited return. One of the auditors, Jeffrey Jones, is suspected of being too lenient with persons whose returns are being audited. For a simple random sample of 30 of the returns audited by Mr. Jones last year, an average of $340 in extra taxes was collected.
Required:
Assuming a normal population of extra taxes collected with a standard deviation of $90, do the suspicions against Mr. Jones appear to be justified?
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the justification against Mr. Jones appears not to be justified
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 356[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = \$340[/tex]
The standard deviation is [tex]\sigma = \$ 90[/tex]
The null hypothesis is [tex]H_o : \mu = \$ 35 6[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne \$ 35 6[/tex]
Let assume the significance level is [tex]\alpha = 0.05[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 340 - 356 }{\frac{90 }{\sqrt{30} } }[/tex]
=> [tex]t =-0.9737 [/tex]
Generally the sample size from the question is small that it is not greater than 30 hence we use t-test
Now the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 30- 1[/tex]
=> [tex]df= 29[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 P (t > -0.9737 )[/tex]
Generally from the t-distribution table , the probability of -0.9737 at a degree of freedom of [tex]df= 29[/tex] for a two -tailed test is
[tex]P (t > -0.9737 ) = 0.33825793[/tex]
Hence p-value is
[tex]p-value = 2*0.33825793[/tex]
[tex]p-value = 0.676 [/tex]
From the value we obtained we see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the justification against Mr. Jones appears not to be justified
On an architect's blueprint, 1 inch corresponds to 2 feet. Find the length of a wall represented by a line 2 1/2 inches long on the blueprint
What is equal to d? I’m sorry but I need help.
(x+5) (x+4) give me the answers quick please
[tex] \red { \orange {\boxed {\boxed{Answers}}}}[/tex]
[tex] = (x + 5)(x + 4)[/tex]
[tex] = {x}^{2} + 4x + 5x + 20[/tex]
[tex] = {x}^{2} + 9x + 20[/tex]
What is the measure of angle b?
Answer:
if those lines are parallel, then the m∠ = 92°
Step-by-step explanation:
The angle rule of corresponding angles or the corresponding angles postulate states that the corresponding angles are equal if a transversal cuts two parallel lines. Corresponding angles are equal if the transversal line crosses at least two parallel lines.
oliver runs a mile in 6 minutes. he left his house and ran 2 miles north, 3 miles east, then run back to his house. what was the total distance of olivers run
Answer:
10 miles
Step-by-step explanation:
You add 2+3+2+3 which equals 10. The information about him running a mile in 6 minutes is completely irrelevant, they did that to confuse you.
pls help meeeeeeeeeeee!!
Answer:
45 with a remainder of 27.
Step-by-step explanation:
Hope this helps you! Good luck! <3
If f(x) and its inverse function, f'(x), are both plotted on the same coordinate plane, what is their point of
intersection?
Answer:
The plot coordinates are (3,3).
Step-by-step explanation:
Given:
A function f(x) and its inverse is f-1(x)
To find :
The plot of the coordinates for the intersection.
Solution:
Now we know that inverse function is changing the y=f(x) and then
changing to x to y and y to x
So given function is f(x)
Inverse function is y,
But value of inverse function is f-1(x)
So y=f(x)=f-1(x)
Therefore it becomes
y=x
Hence the value is y=x coordinates
Suppose that Haley encounter two traffic lights on her commute to GGC campus. Based on
her past experience, she judge that the probability is 0.35 that the first light will be red when she gets to it,
0.45 that the second light will be red, and 0.20 that both lights will be red. Let R1 denote the event that the
first light is red, and let R2 denote the event that the second light is red.
a) Determine the probability that at least one light will be red. (Show how you calculate this.)
b) Determine the conditional probability that the second light will be red given that the first light is
red. (Show how you calculate this.)
c) Are the events R1 and R2 independent? Justify your answer numerically.
d) Are the events R1 and R2 disjoint (mutually exclusive)? Justify your answer numerically.
Answer:
Explained below.
Step-by-step explanation:
The information provided is,
P (R₁) = 0.35
P (R₂) = 0.45
P (R₁ ∩ R₂) = 0.20
(a)
Compute the probability that at least one light will be red as follows:
P (at least one light will be red) = P (R₁ ∪ R₂)
= P (R₁) + P (R₂) - P (R₁ ∩ R₂)
= 0.35 + 0.45 - 0.20
= 0.60
Thus, the probability that at least one light will be red is 0.60.
(b)
Compute the conditional probability that the second light will be red given that the first light is red as follows:
[tex]P(R_{2}|R_{1})=\frac{P(R_{1}\cap R_{2})}{P(R_{1})}[/tex]
[tex]=\frac{0.20}{0.35}\\\\=0.571428\\\\\approx 0.57[/tex]
Thus, the conditional probability that the second light will be red given that the first light is red is 0.57.
(c)
If two events, say A and B are independent then:
P (A|B) = P (A).
The value of P (R₂ | R₁) = 0.57.
And the value of P (R₂) = 0.45
P (R₂ | R₁) ≠ P (R₂)
Thus, the events R₁ and R₂ are not independent.
(d)
If two events, say A and B are mutually exclusive then:
P (A ∩ B) = 0
The value of P (R₁ ∩ R₂) = 0.20.
Thus, the events R₁ and R₂ are not mutually exclusive.
divide 25.84 divide by 4
Answer:
25.84 divide by 4 Is 6.46.
Charlie has 468 onions to sell. He puts 12 onions in each bag, and he sells the bags for $8 each. What is the answer?
Answer:
312 $
Step-by-step explanation:
468 / 12 = 39 bags
8 x 39 = 312 $
so the answer is 312$
In a certain chemical, the ratio of zinc to copper is 4 to 17. A jar of the chemical contains 714 grams of copper. How many grams of zinc does it contain?
It contains
grams of zinc
Answer:
z= 168
Step-by-step explanation:
proportion zinc to copper = 4/17
4/17 = z/ 714
17 • z = 4 • 714
17 • z = 2856
z= 2856/17
z = 168
Answer:
60
Step-by-step explanation:
Is it possible to partition an arbitrary right triangle into isosceles triangles? Justify your answer.
please answer asap :)
Answer:
yes
Step-by-step explanation:
An arbitrary right triangle can be partitioned into isosceles triangle by drawing a median from the right angle to the hypotenuse.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Let's take a right angled triangle ΔABC.
Let C be the right angle in this triangle.
Then AB will be the longest side of the triangle, which is the hypotenuse.
Median of a triangle is the line segment joining the vertex to the midpoint of the opposite side of the triangle.
Suppose we draw a median from C to the midpoint of AB intersecting AB at a point P.
Then there are two triangles formed ΔAPC and ΔBPC.
AP = BP since P is the midpoint of AB.
PC = PC is the common side for both triangles.
So ΔAPC and ΔBPC are isosceles triangles, because two sides are equal.
Hence any right triangle can be partitioned into two isosceles triangles this way.
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The graph of a quadratic function with vertex (3,2) is shown in the figure below.
Find the domain and the range.
Answer:
Domain=All Real Numbers Range=y>2
Step-by-step explanation:
Since the graph expands infinitely across the x axis it is all real numbers
Since the Y covers all the numbers above 2 it is y>2
Identify next 3 numbers in this sequence 2,6,3,9,6,18,15
A number plus it’s opposite is ___ zero. always,sometimes,never
Answer:
always
Step-by-step explanation:
Which of the following is equal to 7%?
O A. A
O B. 73
O C. 173
O D.
SUBMIT
The decimal equivalent of 7% is, C. 0.07.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
We know, Percentages and decimals are related to each other.
Decimals can be converted into percentages by multiplying them by 100
and vice versa.
Given, We have to find the decimal equivalent of 7%.
The decimal equivalent of 7% is,
= 7/100.
= 0.07.
Q. Which of the following is equal to 7%?
A. 7.
B. 0.7.
C. 0.07.
D. 7%.
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Last year, 50 students attended the winter carnival. This year, 60 students attended the carnival. Which statement below correctly describes the percent
change from last year to this year?
A
An increase of 10%
B
A decrease of 10%
С
An increase of 20%
D
A decrease of 20%
Answer:
C. An increase of 20%
Step-by-step explanation:
50/100 = 60/x
Cross products
50 x = 6000
Divide 50 by both sides
x = 120
60 is 120% of 50, so there is a 20% increase
Hope this helps!
-Jerc
The manager of a restaurant determined that the odds against a customer ordering dessert are 11/12 . What is the probability of a customer ordering dessert?
Answer:
1 out of 12
Step-by-step explanation:
12-11=1
Eloise practiced piano for 25 of an hour. Sarah practiced piano for 34 of an hour.
How much longer did Sarah practice than Eloise?
Answer:
34 - 25 = 9
Step-by-step explanation:
guys they meant 2/5 and 3/4...
In a study of the effect of aluminum intake on the mental development of infants, a group of 54infants who had been born prematurely were given a special aluminum depleted intravenous-feeding solution. At an adjusted age of 18 months,the neurologic development of the infants were measured using the Bayley Mental Development Index (BMDI), a unitless scale with higher scores indicating higher development. They had a sample mean BMDI of 97.4 and a sample standard deviation of 18.0.The (BMDI) is similar to an IQ score, with 100 being the average in the general population.
Assuming all relevant assumptions are met, carry out the appropriate testto determine if infants who receivedthealuminum depleted intravenous-feeding solution had a significantly differentaverage BMDI score thaninthe general population. Be sure to include all the stepsfor full credit.
Given:critical value= = 2.00
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
The no sufficient evidence to conclude that the average BMDI score is different from the general population
Step-by-step explanation:
From the question we are told that
The sample size is n = 54
The sample mean is [tex]\= x = 97.4[/tex]
The standard deviation is [tex]s = 18.0[/tex]
The population mean is [tex]\mu = 100[/tex]
The critical value is [tex]t_{critical } = 2.0[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu}{\frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 97.4 - 100}{\frac{ 18}{\sqrt{54} } }[/tex]
=> [tex]t =-1.062[/tex]
Comparing the obtained t statistics with the critical value we see that
The critical value is not within the region of rejection (i.e -1.062 to 1.062 )
Hence the decision rule is
Fail to reject the null hypothesis
The conclusion is
The no sufficient evidence to conclude that the average BMDI score is different from the general population
Siobhan earned $45 babysitting on Friday. On Saturday, she babysat for 5 hours at $4 per hour. On Sunday she bought a DVD for $32. How
much money did she have left after buying the DVD?
$30
Work: 45+20=65
65-35=30
You are playing a video game. For each diamond you collect, you earn 110 points. You also earn 80 bonus points by completing the level in less than 2 minutes. You need to earn more than 1620 points to continue on to the next level. Write and solve an inequality that represents the numbers d of diamonds you must collect in less than 2 minutes to advance to the next level.
Answer:
110d + 80 > 1620
d > 14
Step-by-step explanation:
The amount of points from collecting diamonds can be represented by 110d, since you get 110 points for each diamond, d
Add 80 to this to represent the bonus points.
Use a greater than inequality, because you have to get more than 1620 points.
Put this all together:
110d + 80 > 1620
Then, solve for d:
110d + 80 > 1620
110d > 1540
d > 14
So, you have to collect more than 14 diamonds in less than 2 minutes in order to advance to the next level.
Maria makes money
by commission rates.
She gets 15% of
everything she sells. If
Maria sold $23,000
worth of items this
month, what is her
salary for the month?
Show your work on
the slide!
Answer:
Monthly salary = $3450
Step-by-step explanation:
In this problem, it is given that, Maria gets 15% of everything she sells. If Maria sold $23,000 worth of items this month, we need to find her salary for the month.
It means we need to find the 15% of $23,000 to find her salary. Let the salary be x.
ATQ,
[tex]x=15\%\ \text{of}\ 23000\\\\x=\dfrac{15}{100}\times 23000\\\\x=\$3450[/tex]
Hence, her salary for the month is $3450.
Salary of Maria for the month is $3,450
Given that;
Amount of item sold by Maria = $23,000
Percentage of commission = 15%
Find:
Salary of Maria for the month
Computation:
Salary of Maria for the month = Amount of item sold by Maria × Percentage of commission
Salary of Maria for the month = $23,000 × 15%
Salary of Maria for the month = $3,450
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People living in a society where one person rules by force have which type of government?
Answer:
An autocracy is a government structure in which the ultimate political authority is concentrated in one person's hands.
Hope this helps please give me brainliest!
God bless!
An autocracy.
An autocracy is a system of government in which a supreme political power is concentrated in the hands of one person.
Select the values that correctly complete the problem. a = b = c = d = e =
Answer: 2/3 = b/ac = d/e
Step-by-step explanation:
This is all I got if I got it right. Is this one of your answers?
Answer:
a= 2
b=4
c=3
d=2
e=3
Step-by-step explanation:
i hope this helps.
Express the percent as a decimal. { 98% }
Answer:
98.
Step-by-step explanation:
Answer:
0.98 would be the 98% as a decimal
All of the following represent the same function except
All of the aforementioned represent the same function except: C. {(0, 1), (2, 3), (4, 5), (7, 8)}.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.
The types of function.In Mathematics, there are different types of function and these include the following;
Modulus functionSignum functionPeriodic functionInverse functionPiece-wise defined function.Logarithm functionFrom the first mapping, we can logically deduce the following:
when x = 1, y = 0
y = x - 1
0 = 1 - 1
when x = 3, y = 2
y = x - 1
2 = 3 - 1
when x = 5, y = 4
y = x - 1
4 = 5 - 1
when x = 8, y = 7
y = x - 1
7 = 8 - 1
For the ordered pair, we have:
when x = 0, y = 1
y = x + 1
1 = 0 + 1
when x = 2, y = 3
y = x + 1
3 = 2 + 1
when x = 4, y = 5
y = x + 1
5 = 4 + 1
Therefore, the function for these ordered pairs is equal to y = x + 1.
For the table of value, we have:
when x = 1, y = 0
y = x - 1
0 = 1 - 1
In this context, we can reasonably infer and logically deduce that all of the aforementioned represent the same function except {(0, 1), (2, 3), (4, 5), (7, 8)}.
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the set
of whole number less than 20
Answer:
maybe 3, 6, 9, 12, 15, 18?
Step-by-step explanation:
sorry if this doesn't help but I hope someone else can help you! good luck
What is the solution to the equation 7,- 5* ++5
-
16
ff - 25?
h = 11
3
h = 5
h = 7
6
21
2
Answer:
the answer to the problem is h=7