Answers
(B)
Step-by-step explanation:
The graph has zeros at x = -5 and x = 3 and passes through (4, 9). We can write the equation for the graph as
[tex]y = (x + 5)(x - 3) + c[/tex]
Since the graph passes through (4, 9), we can solve for c, which gives us c = 0. Therefore, the equation for the graph is
[tex]y = (x + 5)(x - 3) = x^2 + 2x - 15[/tex]
Answer:
Step-by-step explanation:
The answer is B) y= x^2+2x-15
Related Questions
Find the simple interest on the following. 1 ) Rs 1,760 for 3 years 6 months at the rate of 12% p.a.
Plss help me
Answers
Answer:
739.2
Step-by-step explanation:
Select the correct answer. Which function is continuous across Its domain
Answers
Answer:
D is the answer
Step-by-step explanation:
plug the -2's in line 1 & 2 then 4 in 2 and 3
the 1&2 , and the 2 and 3 numbers have to match
Using the conditions for continuity, we find that the function D.) is continuous.
How to check if a function is continuous?A function f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied:
f(a) exists (i.e. the value of f(a) is finite)the right-hand limit = left-hand limit, and both are finite.right-hand limit = left-hand limit = f(a)Since for -4 <= x < -2, -2 <= x < 4 and 4 <= x <= 8, the function f(x) is defined by straight lines , the function will be continuous for all x ≠ -2 and 4. Now for x = -2, 4, let us check all the three conditions:
A.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 6 = 4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
B.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 -2 = -4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
C.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 25 - 3*4 = 13
left hand limit = 0.5 * (4)² = 8
right hand limit = 25 - 3*4 = 13
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = 4.
D.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 20 - 3*4 = 8
left hand limit = 0.5 * (4)² = 8
right hand limit = 20 - 3*4 = 8
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = 4.
Thus, the function is continuous.
Learn more about continuity here
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What are the solutions to the system of equations graphed below
Answers
A marketing researcher wants to test the hypothesis that, within the population, there are differences in the importance attached to shopping by consumers living in the northern, southern, eastern and western United States. Which statistical test should be used
Answers
Answer: Analysis of variance
Step-by-step explanation:
Analysis of variance is the statistical test that's used in analyzing the differences among means. The analysis of variance is used to determine if a statistically significant differences exust between the means of the independent groups.
Based on the question given, the null hypothesis will be that no difference in the importance that's attached to shopping by the consumers living in different regions in the United States.
Which of the following is true?
1. The scale factor is 5/2 with a center of dilation at point B. The image of AB is on the same line because it passes through the center of dilation and CD is parallel to its image because it does not pass through the center of dilation.
2. The scale factor is 5/2 with a center of dilation at point B. The image of AB is on the same line because it does not pass through the center of dilation and CD is parallel to its image because it does pass through the center of dilation.
3. The scale factor is 2/5 with a center of dilation at point B. The image of AB is on the same line because it does not pass through the center of dilation and CD is parallel to its image because it does pass through the center of dilation.
4. The scale factor is 2/5 with a center of dilation at point B. The image of AB is on the same line because it passes through the center of dilation and CD is parallel to its image because it does not pass through the center of dilation.
Answers
Answer:
Option A
Step-by-step explanation:
If the quadrilateral ABCD is dilated by a scale factor 'k' to form quadrilateral A'B'C'D',
Scale factor = [tex]\frac{\text{Length of one side of the Image}}{\text{Length of one side of the original}}[/tex]
k = [tex]\frac{BA'}{BA}[/tex]
Distance between B(2, -5) and A(-1, -1) = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(2+1)^2+(-5+1)^2}[/tex]
= 5 units
Distance between B(2, -5) and A'(-5.5, 5) = [tex]\sqrt{(-5.5-2)^2+(5+5)^2}[/tex]
= [tex]\sqrt{(-7.5)^2+(10)^2}[/tex]
= 12.5 units
Scale factor 'k' = [tex]\frac{12.5}{5}[/tex]
k = [tex]\frac{5}{2}[/tex]
Therefore, ABCD is dilated by a scale factor [tex]\frac{5}{2}[/tex] about point B.
BA and it's image BA' are on the same line and passes through center of dilation B.
Similarly, lines CD and C'D' will be parallel because they do not pass through center of dilation.
Therefore, Option (A) will be the correct option.
what type of number cannot be written as a fraction p/q, where p and q are intergers and q is not equal to zero
Answers
Answer:
irrational numbers
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.
Hi there!
»»————- ★ ————-««
I believe your answer is:
Irrational Number
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
The definition that is given in the question was the definition of a irrational number.A number that cannot be written as a fraction with two integers is called a irrational number. Some examples of irrational numbers are non-terminating decimals that do not repeat and non-perfect squares. A number that CAN be written as a fraction with two integers is called a rational number.⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
2+8+5+9+90=
3+45+111=
Answers
Answer:
1) 114
2) 159
Step-by-step explanation:
2+8+5+9+90 = 114
3+45+111 = 159
Hope this helps.
Answer:
1)144
2)159
..........
when a number is added to 1/5 of itself, the result is 24. the equation that models this problem is n+1/5n=24. what is the value of n?
Answers
1
5
n
=
24
⇒
5
n
+
n
5
=
24
⇒
6
5
n
=
24
⇒
n
=
24
×
5
6
⇒
n
=
20
The ratio of the number of cherry tomatoes in a tossed salad to people served is 7:15. If Waldo wants to serve 105 people, how many cherry tomatoes will Waldo use
Answers
First the store raised the price of a pot by 20%. Then they announced a 20% discount on the pot. Is the customer going to pay more or less for the pot now than before.
Answers
Answer:
less
Step-by-step explanation:
An increase of 20% makes the price 120% of the original price.
A discount of 20% makes the discounted price 80% of the previous price.
Original price: x
20% increase in price: 1.2 * x
20% discount over the raised price: 0.8 * 1.2 * x
Now we multiply the numbers in the last expression and compare the result with x.
0.8 * 1.2 * x = 0.96x
0.96 is less than x, so the customer pays less than the original price.
The slope of diagonal AB is ___ , and it’s equation is ___.
Answers
Answer:
The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].
Step-by-step explanation:
Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.
Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].
Ivan is playing a skee-ball game. Different points are awarded depending on which hole the ball goes through. When the ball goes in the smallest hole, it is worth 100 points. When it goes in the bigger hole, it is worth 10 points, and when it does not go in either hole, it is worth 1 point. Ivan earned 352 points in the last game.
Which combination will result in a score greater than his current score?
2 balls in the smallest hole, and 8 balls in the bigger hole
4 balls in the smallest hole, and 6 balls in neither hole
3 balls in the smallest hole, 4 balls in the bigger hole, and 3 balls in neither hole
3 balls in the smallest hole, 3 balls in the bigger hole, and 4 balls in neither hole
Answers
Answer:
B.
Step-by-step explanation:
I don't know for a fact but i think its B. Sorry if I got it wrong.
A table is on sale for $247, which is 76% of the regular price.
What is the regular price?
Answers
Answer:
$325
Step-by-step explanation:
Find the regular price by dividing 247 by 0.76:
247/0.76:
= 325
So, the regular price was $325
Matthew participates in a study that is looking at how confident students at SUNY Albany are. The mean score on the scale is 50. The distribution has a standard deviation of 10 and is normally distributed. Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?
a) 93.32%
b) 6.68%
c) 0.07%
d) 43.32%
Answers
Answer:
b) 6.68%
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean score on the scale is 50. The distribution has a standard deviation of 10.
This means that [tex]\mu = 50, \sigma = 10[/tex]
Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?
The proportion is 1 subtracted by the p-value of Z when X = 65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 50}{10}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
1 - 0.9332 = 0.0668
0.0668*100% = 6.68%
So the correct answer is given by option b.
Midwest Publishing publishes textbooks. The company uses an 800 number where people can call to ask questions about the textbooks and place orders. Currently, there are 2 representatives handling inquiries. Calls occurring when both lines are in use get a busy signal. Each representative can handle 12 calls per hour. The arrival rate is 20 calls per hour.
Required:
a. How many extension lines should be used if the company wants to handle 90% of the calls immediately?
b. What is the probability that a call will receive a busy signal if your recommendation in part (a) is used?
c. What percentage of calls receive a busy signal for the current telephone system with two extension lines?
Answers
Answer:
A. 18 calls
B. 0.9
C. 20
Step-by-step explanation:
Number of representatives=2,
Number of extension lines=2,
Average calls each representative can accommodate per hour = 15 calls,
Arrival rate per hour = 30 calls
(a) 90% of the arrival rate = 0.09 × 20 = 18 calls
To handle 18 calls immediately, 18 extension lines should be used
(b) Probability is given by number of possible outcomes ÷ number of total outcomes
Number of possible outcomes = 18, number of total outcomes = 20
Probability (call will receive busy signal) = 18/20 = 0.9
(c) For one extension line, numbers of calls to receive busy signal = 20 - 10 = 10 calls
Number of calls to receive busy signal for the current telephone system with two extension lines = 2 × 10 = 20 calls
csc(π/2) =__
a.0
b.-1
c.1
d.undefined
Answers
Hi there!
[tex]\large\boxed{C. \text{ } 1}[/tex]
csc (π/2)
π/2 is located at (0, 1)
csc is equal to 1/y, or the reciprocal of the y-value
Therefore:
csc(π/2) = 1/1 = 1. C is the correct answer.
A small radio transmitter broadcasts in a 69 mile radius. If you drive along a straight line from a city 93 miles north of the transmitter to a second city 78 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Answers
Answer:
See Explanation
Step-by-step explanation:
According to the Question,
We have A small radio transmitter that broadcasts in a 69-mile radius. If you drive along a straight line from a city 93 miles north of the transmitter to a second city 78 miles east of the transmitter.Thus,
The distance that you get reception is the length of the chord created by the intersection of the circle defining the edge of transmission and the line defining the car trip.
x2 + y2 = 69² this is the circleAnd,
The Transmitter at the origin
City to the north at (0,93) & City to the east at (78,0)
the Slope is M=(-93/78)
Intercept is B= y - mx ⇒ 93 - (-93/78)(0) = 93
The equation of the line between the cities is y = (-93/78)x + 93
y = -93x/78 + 93 this is the lineNow, Solve the above two Equations
The intersection is gotten from the picture or solving:
x^2 + [(-93/78)*x + 93]^2 = 69^2
on solving we get, the points approximately are: (67.952,11.98 ) and (23.6277, 64.82)Now,
From the Pythagorean theorem the total distance of the trip is:
d1 = √(93^2 + 78^2) ≈ 121.37miles
And the distance when the signal is picked up is:
d2 =√ [(67.952-23.627)^2 + (64.82 - 11.98)^2] ≈ 68.96 miles
You will pick up a signal from the transmitter in (d2/d1)*100 = 56% of the drive.
State sales tax y is directly proportional to retail price x. An item that sells for 156 dollars has a sales tax of 14.42 dollars. Find a mathematical model that gives the amount of sales tax y in terms of the retail price x .
What is the sales tax on a 320 dollars purchase.
Answers
Answer:
The sales tax on a 320 dollars purchase is of $29.6.
Step-by-step explanation:
State sales tax y is directly proportional to retail price x.
This means that:
[tex]y = cx[/tex]
In which c is the constant of proportionality.
An item that sells for 156 dollars has a sales tax of 14.42 dollars.
This means that [tex]x = 156, y = 14.42[/tex]. We use this to find c. So
[tex]y = cx[/tex]
[tex]14.42 = 156c[/tex]
[tex]c = \frac{14.42}{156}[/tex]
[tex]c = 0.0924[/tex]
Then
[tex]y = 0.0924x[/tex]
What is the sales tax on a 320 dollars purchase?
y when [tex]x = 320[/tex]. So
[tex]y = 0.0924(320) = 29.6[/tex]
The sales tax on a 320 dollars purchase is of $29.6.
Help plz I just need the awnser to this question
Answers
Answer:
A seems to be correct
Step-by-step explanation:
The value of y varies with x and z, and y=8, when x=4 and z=10. What is the value of y when x=5 and z=11
Answers
Help me please with this maths question thank you
Answers
Answer:
Step-by-step explanation:
A)
The opposite sides of a rectangle are equal. The width make this obvious because both of them are x.
B)
The lengths are not so obvious, but it is never the less true. The two sides are obvious and they are therefore true.
4x + 1 = 2x + 12 Subtract 1 from both sides.
- 1 -1
4x = 2x + 11 Subtract 2x from both sides
-2x -2x
2x = 11 Divide by 2
x = 11/2
x = 5.5
C)
P = L + L + w + w
P = 4(5.5) + 1 + 2(5.5) + 12 + 5.5 + 5.5
P = 22 + 1 + 11 + 12 + 11
P = 23 + 23 + 11
P = 57
Jason wants to fill a cylindrical water tank to its full capacity. He knows that the volume of the tank is equal to the product of , the square of the radius of the tank, and the height of the tank. Jason measured the height of the tank and found it to be 15 feet. He also measured the radius of the cylindrical tank and found it to be 10 feet. If Vrepresents the volume of the cylindrical tank, then which of the following equations can be used to calculate the volume of the tank?
Answers
Answer:
B) [tex]\sqrt{\frac{v}{15\pi } } = 10[/tex]
Step-by-step explanation:
Find the area of the irregular figure. Round to the nearest hundredth.
Answers
Answer:
[tex]67.5\text{ [square units]}[/tex]
Step-by-step explanation:
The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.
Formulas:
Area of rectangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=bh[/tex] Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]By definition, the base and height must intersect at a 90 degree angle.
The rectangle has a base of 10 and a height of 5. Therefore, its area is [tex]A=10\cdot 5=50[/tex].
The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 2\cdot 5=5[/tex].
Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 5\cdot 5=12.5[/tex].
Thus, the area of the total irregular figure is:
[tex]50+5+12.5=\boxed{67.5\text{ [square units]}}[/tex]
Simplify your answer
Answers
Answer:
= F^2 x^2
Step-by-step explanation:
(F(x))^2
Apply the rule: (a) =a (x) = x
= (Fx)^2
Apply exonent rule: (a . b)^n = a^n b^n (Fx)^2 = F^2 x^2
= F^2 x^2
Find the union {6, 11, 15} U Ø
Answers
Explanation:
The Ø means "empty set". It's the set with nothing inside it, not even 0.
We can write Ø as { } which is a pair of curly braces with nothing between them.
The rule is that if we union any set A with Ø, then we'll get set A
A U Ø = A
Ø U A = A
In a sense, it's analogous to adding 0. So it's like saying A+0 = A and 0+A = A.
So that's why {6, 11, 15} U Ø = {6, 11, 15}
There's nothing to add onto the set {6, 11, 15}, so we just get the same thing back again.
A statistician calculates that 8% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
Answers
Answer:
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A statistician calculates that 8% of Americans own a Rolls Royce.
This means that [tex]p = 0.08[/tex]
Sample of 595:
This means that [tex]n = 595[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.08[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.08*0.92}{595}} = 0.0111[/tex]
What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?
Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.
Probability the proportion is less than 5%:
P-value of Z when X = 0.05. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.05 - 0.08}{0.0111}[/tex]
[tex]Z = -2.7[/tex]
[tex]Z = -2.7[/tex] has a p-value of 0.0035
2*0.0035 = 0.0070
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
Find the interquartile range of the data set represented by this box plot.
25
20
45
35
Answers
Answer:
25
Step-by-step explanation:
im pretty sure i think only ok i think no saying bad things in the comment
Solve the given system by the substitution method
5x + y 19
7x-2y = 13
Answers
Answer:
x = 3 , y = 4
Step-by-step explanation:
5x + y = 19 --------- ( 1 )
=> y = 19 - 5x
7x - 2y = 13 ------------ ( 2 )
Substitute y in ( 2 ) :
7x - 2( 19 - 5x ) = 13
7x - 38 + 10x = 13
17x = 13 + 38
17x = 51
x = 3
Substitute x in ( 1 ) :
5x + y = 19
5( 3 ) + y = 19
15 + y = 19
y = 19 - 15
y = 4
If ABC is reflected across the y-axis, what are the coordinates of C?
A. (-8, -4)
B. (8,-4)
C. (-8,4)
D. (4,-8)
Answers
Answer:
c....................
The sum of the first ten terms of an arithmetic progression consisting of
positive integer terms is equal to the sum of the 20th, 21st and 22nd term.
If the first term is less than 20, find how many terms are required to give
a sum of 960.
Answers
Answer: [tex]n=13[/tex]
Step-by-step explanation:
Given
Sum of the first 10 terms is equal to sum of 20, 21, and 22 term
[tex]\Rightarrow \dfrac{10}{2}[2a+(10-1)d]=[a+19d]+[a+20d]+[a+21d]\\\\\Rightarrow 5[2a+9d]=3a+60d\\\Rightarrow 10a+45d=3a+60d\\\Rightarrow 7a=15d[/tex]
No of terms to give a sum of 960
[tex]\Rightarrow 960=\dfrac{n}{2}[2a+(n-1)d]\\\\\Rightarrow 1920=n[2a+(n-1)\cdot \dfrac{7}{15}a]\\\\\Rightarrow 28,800=n[30a+7a(n-1)]\\\\\Rightarrow a=\dfrac{28,800}{n[30+7n-7]}\\\\\Rightarrow a=\dfrac{28,800}{n[23+7n]}[/tex]
Value of first term is less than 20
[tex]\therefore \dfrac{28,800}{n[23+7n]}<20\\\\\Rightarrow 28,800<20n[23+7n]\\\Rightarrow 0<460n+140n^2-28,800\\\Rightarrow 140n^2+460n-28,800>0\\\\\Rightarrow n>12.79\\\\\text{For integer value }\\\Rightarrow n=13[/tex]
Answer:
15
Step-by-step explanation:
In the previous answer halfway through they used the equation: 960 = (n÷2)×(2a+(n-1)×(7a÷15))
Using this equation we can substitute an number to replace n, the higher the number is the smaller a would be.
When we substitute 15 into a, then it leaves us with the answer to be a = 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.
To double check this answer you can find that d = 7 by changing the a into 15 in the formula 7a/15 (found in the previous answer.
Then in the expression: (n÷2)×(2a+(n-1)×d)
substitute:
n = 14 (must be an even number for the equation to work)
a = 15
d = 7
This will give you an answer of 847, but this is only 14 terms as we changed n into 14. To add the final term you need to complete the following equation: 847+(a+(n-1)×d)
substituting:
n = 15
a = 15
d = 7
This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.
I hope this has helped you.
P.S. Everything in the previous solution was right apart from the start of the last section and the answer