Select the correct answer.
The graph of function f is shown.

The graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercepts the x-axis at minus 2 units and y-axis at 2 units

Function g is represented by the table.

x -2 -1 0 1 2
g(x) -2/3 0 2 8 26

Which statement correctly compares the two functions?

A. They have the same x-intercept and the same end behavior as x approaches ∞.
B. They have the same y-intercept and the same end behavior as x approaches ∞.
C. They have the same x- and y-intercepts.
D. They have different x- and y-intercepts but the same end behavior as x approaches ∞.

Answer: 170.6

Step-by-step explanation:

you have to find the cube root of 512 which will get you 170.6

which is not a perfect cube

Answer is 19

Step-by-step explanation:

Answer:

What??

Step-by-step explanation:

The distance between the points is 4.3.

Given the points are C(2,4) and D (5,7)

let the two points be:

C (2,4) = (x₁ , y₁)

D (5,7) = (x₂ , y₂)

The length of the section of a line connecting any two places represents their distance. Only one line connects the two places, and it passes through both. The length of the line segment that connects the two places may therefore be used to compute the distance between them.

Distance between the points = √(x₂ ₋ x₁)² ₊ (y₂ ₋ y₁)²

substitute the points.

d = √(5 ₋ 2)² ₊ (7 ₋ 4)²

d = √(3)² ₊ (3)²

d =  √9 ₊ 9

d =  √18

d = 4.24

rounding off to nearest tenth

d = 4.3

Hence we get the distance between two points as 4.3.

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To sketch the curve with polar equation θ = −π/6, we need to plot all the points (r, θ) that satisfy the equation for various values of r. Since θ is fixed at −π/6, all the points will lie on a line at an angle of −π/6 to the positive x-axis.

The value of r can be positive or negative, so we will plot points both above and below the x-axis.

Since r can be any value, we will just choose a few values for illustration purposes. Let's choose r = 1, 2, −1, and −2. Then the corresponding points are:

(1, −π/6), (2, −π/6), (−1, −π/6), and (−2, −π/6)

We can plot these points on a polar coordinate system as follows:

These points lie on a line at an angle of −π/6 to the positive x-axis, as expected. Note that the sign of r determines whether the point lies above or below the x-axis.

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A sample size of 60 schoolgirls would be needed to estimate the mean IQ score within +5 points with 99% confidence.

Define mean ?

In statistics, the mean is a measure of central tendency that represents the average value of a set of numbers.

To estimate the required sample size to estimate the mean IQ score within +5 points with 99% confidence, we can use the formula:

\(n = (z^* * \sigma / E)^2\)

Where:

n = required sample size

z* = z-score corresponding to the desired confidence level (99% confidence level in this case, z* = 2.576)

σ = standard deviation of the population (given as 15 in this case)

E = margin of error (desired precision or half the confidence interval, which is 5 in this case)

Substituting the values into the formula, we get:

\(n = (2.576 * 15 / 5)^2\)

\(n = (38.64 / 5)^2\)

\(n = (7.728)^2\)

n ≈ 59.62

Rounding up to the nearest whole number, the required sample size is 60 schoolgirls.

Therefore, a sample size of 60 schoolgirls would be needed to estimate the mean IQ score within +5 points with 99% confidence, assuming a standard deviation of 15 in the population.

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The complete question is :

Estimating mean IQ. IQ scores are typically Normally distributed within a homogeneous population. How large a sample of schoolgirls in Example 14.3 (page 354) would be needed to estimate the mean IQ score u within +5 points with 99% confidence, assuming that o = 15 in this population? (Note that the z multiplier for a 99% confidence level is z* = 2.576.)

10 miles per hour is the average journey speed.

Given that,

Some pupils choose to ride bikes. They move at a 15 mph average speed for the first two hours, and then they stop for lunch for an hour. The pupils ride at a 10 mph speed for an additional hour.

Average speed is ( total distance ) / ( total time )

During the 1st 2 hrs:

distance = speed * time

distance = 15 *2 = 30 miles

During the last hour:

distance = speed * time

distance = 10 *1 = 10 miles

Average speed = 30+10 / 2+1+1 = 40/4 = 10 mil/hr

Therefore, their average speed for the trip is 10 mil/hr

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Answer:

1 is true , 2 is false

Step-by-step explanation:

for equation 2

-2x<8

-2x=8

then we divide both side by coefficient of x which is -2

-2x/-2=8/-2

we will be left with

x= 8/-2

x=-4 which shows that x<-4 and it differs from the second inequality

Answer:

25 ans

Step-by-step explanation:

5 * (100 /20) = 25

so, 20% of 25 is 5

Answer:

x=25

Step-by-step explanation:

0.2x=5

x=25

y equals x times 5 is the answer because 2 times 5 is 10 and so on and so forth hope this helps :D

A linear transformation is a type of function that maps one vector space to another. For a linear transformation to occur, the following must be true:

For all u and v in V and scalars c,

T (u + v) = T (u) + T (v)T (cu) = cT (u)

where V is a vector space and T is a linear transformation. In other words, a linear transformation preserves addition and scalar multiplication. In the given question, let t be a linear transformation from R2 to R2 such that t(1, 0)

= (1, 1) and t(0, 1)

= (−1, 1).To find t(8, 1),

we can do the following:

$$t(8, 1) = t(8 * (1, 0) + 1 * (0, 1))$$$$ t(8, 1)

= 8t(1, 0) + 1t(0, 1)$$$$t(8, 1)

= 8(1, 1) + 1(-1, 1)$$$$t(8, 1)

= (8 - 1, 8 + 1) = (7, 9)$$Therefore, t(8, 1) is equal to (7, 9).

To find t(1, −7), we can do the following:

 $$t(1, -7)

= t(1 * (1, 0) - 7 * (0, 1))$$$$t(1, -7)

= 1t(1, 0) - 7t(0, 1)$$$$t(1, -7)

= 1(1, 1) - 7(-1, 1)$$$$t(1, -7)

= (1 + 7, 1 - 7) = (8, -6)$$Therefore, t(1, −7) is equal to (8, -6).

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Answer:

the answer is 900

Step-by-step explanation:

the 900 will not be necessary

The first number is 11 and second number is 12.We can find by solving two consective numbers.

Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The difference between consecutive numbers is always fixed and it follows a pattern. For example 1, 2, 3 are the first three consecutive natural numbers.

An odd number of consecutive numbers has a whole number as an average. This average is always the middle number. So that means that the sum of the numbers will be Sum = average \times number of consecutive numbers.

Now we find

Let x be a first number and x+1 be a second number.So

x+x+1=23

2x+1=23

2x    =23-1

2x    =22

  x   = 11

x+1= 11+1=12

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The possible values of k are k = 2 and k = -2. These are the values of the constant k for which f(x) is continuous at x = 2.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To determine the values of the constant k for which f(x) is continuous at x = 2, we need to ensure that the left-hand limit, the right-hand limit, and the value of f(x) at x = 2 are all equal.

First, let's find the left-hand limit as x approaches 2. We evaluate the function for x < 2:

f(x) = x² + 5kx    (for x < 2)

Taking the limit as x approaches 2 from the left side (x < 2), we have:

lim(x→2-) f(x) = lim(x→2-) (x² + 5kx) = 2² + 5k(2) = 4 + 10k

Next, let's find the right-hand limit as x approaches 2. We evaluate the function for x > 2:

f(x) = k²x + 4x + 4    (for x > 2)

Taking the limit as x approaches 2 from the right side (x > 2), we have:

lim(x→2+) f(x) = lim(x→2+) (k²x + 4x + 4) = k²(2) + 4(2) + 4 = 2k² + 8 + 4 = 2k² + 12

Now, let's evaluate the value of f(x) at x = 2:

f(x) = 3k² - 4    (for x = 2)

f(2) = 3k² - 4

For f(x) to be continuous at x = 2, the left-hand limit, the right-hand limit, and the value of f(x) at x = 2 should all be equal. Therefore, we set up the following equation:

4 + 10k = 2k² + 12 = 3k² - 4

Simplifying, we have:

2k² + 8 = 3k² - 4

Rearranging the terms, we get:

k² - 12 = 0

Factoring, we have:

(k - 2)(k + 2) = 0

So, the possible values of k are k = 2 and k = -2. These are the values of the constant k for which f(x) is continuous at x = 2.

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Answer:

3:18

Step-by-step explanation:

From 3:12 PM to 5:12 PM it's 3 hours.

From 5:12 PM to 5:30 PM it's 18 minutes.

Total elapsed time: 3:18

I don't know why the question asks "what part of an hour" when the answer is more than 3 hours.

Answer:

\(x\geq -4\)

Step-by-step explanation:

\(3x-9\geq-21\)

add 9 to both sides

\(3x-9+9\geq -21+9\)

\(3x\geq -12\)

divide both sides by 3  

\(\frac{3}{3}x \geq \frac{-12}{3}\)

\(x\geq -4\)

Plot a solid dot on -4 on the number line because the inequality sign is great than or equal to and x the great than or equal to -4.

The arrow is then pointed to the left >>>>

Answer:

45%

Step-by-step explanation:

25% is the same as .25. By taking .25 times 180 you get 45 or 45%.

Answer:

13 units

Step-by-step explanation:

Here we need to use the distance formula.

Hence we get that,

AB =  \(\sqrt{(-8-4)^2 + (4-(-1))^2}\)

AB =  \(\sqrt{(-12)^2 + 5^2}\)

AB =  \(\sqrt{144 + 25}\)

AB =  \(\sqrt{169}\)

AB =  13

The distance between point A(-8,4) and B(4,-1) is 13 units.

The distance between two points of the xy-plane can be found using the distance formula. The distance formula is:

√[(x₂ - x₁)² + (y₂ - y₁)²].

Now the given points are,

A(-8,4) and B(4,-1)

Therefore we have,

x₁ = -8

y₁ = 4

x₂ = 4

y₂ = -1

Now distance between A(1,4) and B(-3,3.5) = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - (-8))² + (-1 - 4)²]

= √[(4 + 8)² + (-5)²]

= √(12² +25)

= √(144 +25)

= √169

= 13 units

Thus, the distance between points A(-8,4) and B(4,-1) is 13 units.

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Answer:

\( \frac{45}{16} \)

To test for differences in full IQ score across the 3 exposure groups, we can use both parametric and non-parametric tests.  Based on the overall test results, if there is sufficient evidence to reject the null hypothesis (p < 0.05), we can perform further pairwise testing between the means.

a) To test for differences in full IQ score across the 3 exposure groups, we can use both parametric and non-parametric tests.

Parametric test (ANOVA):
- Null hypothesis (H0): There are no differences in full IQ score across the 3 exposure groups.
- Alternative hypothesis (Ha): There are differences in full IQ score across the 3 exposure groups.
- Test statistic: F statistic
- P-value: Report the p-value obtained from the ANOVA test.

Non-parametric test:
- Null hypothesis (H0): There are no differences in full IQ score across the 3 exposure groups.
- Alternative hypothesis (Ha): There are differences in full IQ score across the 3 exposure groups.
- Test statistic: Kruskal-Wallis statistic
- P-value: Report the p-value obtained from the Kruskal-Wallis test.

b) To assess the distribution of full IQ scores, we can compare the results of the parametric and non-parametric tests. The test that provides more valid results depends on the assumptions of normality and homogeneity of variances. If the assumptions are met, the parametric test (ANOVA) is more valid. If the assumptions are violated, the non-parametric test (Kruskal-Wallis) is more valid.

c) Based on the overall test results, if there is sufficient evidence to reject the null hypothesis (p < 0.05), we can perform further pairwise testing between the means. Otherwise, if there is not enough evidence to reject the null hypothesis, further pairwise testing is not justified. In either case, the decision should be explained based on the p-value obtained from the overall test.

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To convert meters to inches, we need to know the conversion factor between the two units. The length of a 100-meter soccer field is 3,937 inches.

The conversion factor for meters to inches is 39.37 inches per meter.

Therefore, to convert 100 meters to inches, we can multiply it by the conversion factor:

100 meters × 39.37 inches/meter = 3937 inches

The length of a 100-meter soccer field is 3937 inches.

Expressing the answer in scientific notation, we have:

3937 inches = 3.937 × 10^3 inches.

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Answer: Let's use algebra to solve the problem.

Let x be the number of candy bars Landon bought. We know that:

The cost of the magazine is $5.

The cost of x candy bars is 3x dollars.

The total cost is $23.

We can use these pieces of information to set up an equation:

5 + 3x = 23

Subtracting 5 from both sides, we get:

3x = 18

Dividing both sides by 3, we get:

x = 6

Therefore, Landon bought 6 candy bars.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

F(x) = 4x^2 + 1

G(x) = x^2 - 5

(F-G)(x) = (4x^2+1 - x^2-5)

collect like terms

(F-G)(x) = (4x^2-x^2 + 1-5)

= (3x^2 - 4)

Answer:

Move all terms not containing  x  to the right side of the inequality.

Inequality Form:

x  ≤  9

Step-by-step explanation:

That's the most I can do. I hope this helps! Have a nice day!

Answer:

x ≤ 9

Step-by-step explanation:

C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

\(\bold{\huge{\purple{\underline{ Solution }}}}\)

Show that,

\(\bold{\dfrac{ 2}{2x+11}}{\bold{-}}{\bold{\dfrac{ 1}{x - 4}}}{\bold{=}}{\bold{\dfrac{1}{2}}}\)

Simplifies to,

\(\bold{ 2x² + 3x - 6 = 0 }\)}

Here, We have to show that,

\(\bold{\blue{\dfrac{ 2}{2x+11}}}{\bold{\blue{-}}}{\bold{\blue{\dfrac{ 1}{x - 4}}}}{\bold{\blue{ = }}}{\bold{\blue{\dfrac{1}{2}}}}{\bold{\blue{= 2x² + 3x - 6 = 0}}}\)

\(\bold{\dfrac{ 2}{2x+11}}{\bold{-}}{\bold{\dfrac{ 1}{x - 4}}}{\bold{=}}{\bold{\dfrac{1}{2}}}\)

\(\sf{\dfrac{ 2(x-4) - 1(2x + 11)}{(2x+11)(x-4)}}{\sf{=}}{\sf{\dfrac{1}{2}}}\)

\(\sf{\dfrac{ 2x - 8 - 2x - 11)}{2x(x-4)+11(x - 4)}}{\sf{=}}{\sf{\dfrac{1}{2}}}\)

\(\sf{\dfrac{ - 19 }{2x² -8x + 11x - 44}}{\sf{=}}{\sf{\dfrac{1 }{2}}}\)

\(\sf{\dfrac{ - 19 }{2x² + 3x - 44}}{\sf{= }}{\sf{\dfrac{1}{2}}}\)

\(\sf{ - 19 × 2 = 2x² + 3x - 44}\)

\(\sf{ - 38 = 2x² + 3x - 44 }\)

\(\sf{ 0 = 2x² + 3x - 44 + 38}\)

\(\bold{ 2x² + 3x - 6 = 0 }\)

Hence, It is proved

\(\bold{\dfrac{ 2}{2x+11}}{\bold{-}}{\bold{\dfrac{ 1}{x - 4}}}{\bold{ = }}{\bold{\dfrac{1}{2}}}{\bold{= 2x² + 3x - 6 = 0 }}\).

The required equation has been proved as shown

We are to show that 2/(2x+11) - 1/(x-4) = 1/2

Find the LCM of the expression

\(\frac{2(x-4)-(2x+11)}{(2x+11)(x-4)}=\frac{1}{2}\\ \frac{2x-8-2x-11}{(2x+11)(x-4)}=\frac{1}{2}\\\)

Cross multiply

(2x+11)(x-4) = -19(2)

2x^2 -8x + 11x - 44 = -38

2x^2 + 3x = -38 + 44

2x^2 + 3x = 6

2x^2 + 3x - 6 = 0 (prove)

The required equation has been proved

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Step-by-step explanation:

x2_4=0×2

x2_4+4=0+4

x2=4

x2÷2=4÷2

x=2

Answer:

You don't have a picture

Step-by-step explanation:

Answer:

Hmmm the picture....? Please send it

Answer:

15

Step-by-step explanation:

3x + 2y = 7

y = -3x +11