which expression is equivalent to -1/4 (20z + 24)

Answer:

The second one

O (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)

Step-by-step explanation:

Favorable outcome is the outcome that we are looking for

The outcome that we are looking for when rolling two = die is a sum of 7

The set (1-6) (2-5) (3-4) (4-3) (5-2) (6-1) all add up to equal 7

( 1 , 6 ) 1 + 6 = 7

( 2 , 5 ) 2 + 5 = 7

( 3 , 4 ) 3 + 4 = 7

etc.

Which means that they are the favorable outcomes for rolling a seven

Answer:

[tex]Volume = \frac{3}{128}ft^3[/tex]

Step-by-step explanation:

Given

[tex]Length = 1\ cube[/tex]

[tex]Width = 3\ cubes[/tex]

[tex]Height = 4\ cubes[/tex]

[tex]1\ cube = \frac{1}{8}ft[/tex]

Required

The volume of the cube

Start by calculating the dimension in ft

[tex]Length = 1\ cube[/tex]

[tex]Length = 1 * \frac{1}{8}ft[/tex]

[tex]Length = \frac{1}{8}ft[/tex]

[tex]Width = 3\ cubes[/tex]

[tex]Width = 3 * \frac{1}{8}ft[/tex]

[tex]Width = \frac{3}{8}ft[/tex]

[tex]Height = 4\ cubes[/tex]

[tex]Height = 4 * \frac{1}{8}ft[/tex]

[tex]Height = \frac{1}{2}ft[/tex]

So, the volume is:

[tex]Volume = Length * Width * Height[/tex]

[tex]Volume = \frac{1}{8}ft * \frac{3}{8}ft * \frac{1}{2}ft[/tex]

[tex]Volume = \frac{1}{8} * \frac{3}{8} * \frac{1}{2}ft^3[/tex]

Using a calculator, we have:

[tex]Volume = \frac{3}{128}ft^3[/tex]

Answer:

1

Step-by-step explanation:

First, we can find the equation of the parabola. The standard form of a parabola is ax^2 + bx + c,

where c is the y-intercept. The y-intercept on the graph is -5, and every option starts with x^2, so the equation must be x^2 - 5. This rules out options 3 and 4.

Next, we can find the equation of the line. The options are all given in slope-intercept form: y = mx + b, where b is the y-intercept. The y-intercept on the graph is 1, and option 1 has 1 in the place of b. Therefore, option 1 is the answer.

The true statement over the interval [-3, 0] is: B. average rate of change of function f is less than that of function g.

Over a given interval, the average rate of change of a function is found using the formula: change in y / change in x = f(b) - f(a) / b - a.

Average rate of change of function g over [-3, 0]:

a = -3, f(a) = 5

b = 0, f(b) = 14

Average rate of change = (14 - 5)/(0 - (-3)) = 3

Average rate of change of function f over [-3, 0]:

a = -3, f(a) = -4.5

b = 0, f(b) = 0

Average rate of change = (0 - (-4.5))/(0 - (-3)) = 1.5

Therefore, the correct answer is: B. average rate of change of function f is less than that of function g.

Learn more about average rate of change on:

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Answer:

13

Step-by-step explanation:

4w-10=42

4w=52

w=52/4

w=13

Answer:

[tex]x=15[/tex]

Step-by-step explanation:

Pythagorean theorem: [tex]c^2 = a^2 + b^2[/tex], where c is the longest side (hypotenuse), a and b are the other sides of the right angled triangle.

In this question, c is labelled as [tex]x[/tex].

Therefore, we can use the theorem to find [tex]x[/tex].

[tex]x^2 = a^2+b^2[/tex]

So, substitute in the other sides and solve for [tex]x[/tex].

[tex]x^2 = (9)^2 + (12)^2\\x^2 = 81 + 144\\x^2 = 225\\x = 15[/tex]

We can see the answer is correct because it is meant to be the largest side and [tex]15> 12>9[/tex].

Answer:

Option 4

Step-by-step explanation:

Let any two real number a and b (no matter +ve, -ve or 0). a ≥ b

The average of them will always lie in between them or be equal(if 0).

Let's prove : According to the statement,

a ≥ (a + b)/2 ≥ b

2a ≥ a + b ≥ 2b

2a ≥ a + b and a + b ≥ 2b

a ≥ b and a ≥ b, as we assumed.

Moreover, as the average exists in between a and b, we have the average (a + b)/2. Similarly, there exists one more average of (a + b)/2 and a or b, which definitely lie between a and b as (a + b)/2 lies there and smaller than a and b.

In the same order, we can have many average and the process would stop. This leads to infinite number between a and b.

Notice that we talked about all the numbers moreover there are many irrational(non-terminating like 9.898989.... etc numbers as well.

Option (4), infinite solutions.

Note: we solved for all the number (not specifically odd, even, natural, whole, integer, etc).

Answer:

g(x) is shifted 4 units left and 6 units down from f(x).

Step-by-step explanation:

The parent function is:

f(x).

The child function is:

[tex]g(x) = f(x+4) - 6[/tex]

Transformation 1:

[tex]g(x) = f(x+4)[/tex]

Shifting a function f(x) a units to the left is finding f(x + a). So g(x) = f(x + 4) is f(x) shifted 4 units to the left.

Transformation 2:

[tex]g(x) = f(x+4) - 6[/tex]

Subtracting a function f(x) by a constant a is the same as shifting the function a units down. So subtracting by 6 is shifting the function 6 units down. Thus, the correct answer is:

g(x) is shifted 4 units left and 6 units down from f(x).

Explanation:

The period of a function measures how long a cycle takes. Think of tides on a beach. There's a regular pattern that can be predicted whether its high tide or low tide. Time is often the critical component with the period. Since choice D mentions time and the key term "repeat", this is why it's the answer.

The other values, while useful elsewhere, aren't going to tell us anything about the period. The initial value being 5 doesn't tell us when y = 5 shows up again, and if the function is repeating itself at this point or not. So info about choice A is not sufficient to determine the period. The same goes for choices B and C as well.

Answer:

a <= 3

Step-by-step explanation:

Answer:

2X2

Step-by-step explanation:

Answer: 10

Step-by-step explanation: 5 x 2 = 10

                                             5 + 5 = 10

Answer:

69.12

Step-by-step explanation:

12x5.76

Answer

69

Step-by-step explanation:

12×5.75=69

Answer:

V = πr²h

V = 3.14 (5cm)²(7 cm)

V = 3.14 (25cm²) ( 7 cm)

V = 3.14 (175 cm³)

V = 549.50 cm³

Answer:

a

Step-by-step explanation:

the answer is A I hope that helps you for school

Answer:

42

Step-by-step explanation:

39+39 = 78

162 - 78 = 2 lengths =84

84/2 = 42

Answer:

17.46 ft

Step-by-step explanation:

The inclined plane is in the shape of a right triangle, therefore we can use the Pythagorean theorem to find the length of the inclined plane. The formula for this theorem is the following

[tex]a^{2} + b^{2} = c^{2}[/tex]

Where a and b are the two sides and c is the hypotenuse/inclined side. Therefore, we can simply plug in the lengths of the two sides into the formula and solve for c.

[tex]a^{2} + b^{2} = c^{2}[/tex]

[tex]7^{2} + 16^{2} = c^{2}[/tex]

[tex]49 + 256 = c^{2}[/tex]

[tex]305 = c^{2}[/tex]   ... square root both sides

17.46 = c

Answer:

56.55

Step-by-step explanation:

Solution

V=

π

r

2

h

=

π

3

2

2

≈

56.54867

Answer:

[tex] a^{5} [/tex]

Step-by-step explanation:

Given the mathematical expression;

a⁸/a³

To rewrite the expression in the form [tex] a^{m} [/tex]

We would have to apply the law of indices.

[tex] Law \; of \; division = \frac {a^{x}}{a^{y}} = a^{x - y} [/tex]

[tex] Law \; of \; division = \frac {a^{8}}{a^{3}} = a^{8 - 3} [/tex]

[tex] a^{m} = a^{8 - 3} = a^{5} [/tex]

Step-by-step explanation:

9514 1404 393

Answer:

  C.  y = 11.27(0.7^x)

Step-by-step explanation:

The table value (x, y) = (0, 11.27) tells you the multiplier of the exponential term will be 11.27. The decreasing values tell you the base of the exponential term is less than 1. Only answer choice C matches these requirements.

the clock lost 2 seconds per day

Answer:C. [12.35+(2.25x3)-2]÷3

Answer:

yes it does. good job on your A.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Complete question is;

A leasing firm claims that the mean number of miles driven annually, u , in its leased cars is less than 12800 miles. A random sample of 50 cars leased from this firm had a mean of 12499 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 3140 miles. Is there support for the firm's claim at the 0.05 level of significance?

Perform a one-tailed test.

null hypothesis?

alternative hypothesis?

type of test statistic?

value of the test statistic?

the p-value?

Can we support the leasing firm’s claim that the mean number of miles driven annually is less than 12800 miles?

Answer:

A) Null hypothesis; μ ≥ 12800

Alternative hypothesis; μ < 12800

B) type of test statistic: z-score test

C) test statistic; z = -0.678

D) p - value = 0.2489

E) No, we can't support the leasing firms claim

Step-by-step explanation:

We are given;

Population mean; μ = 12800 miles

Sample mean; x¯ = 12499 miles

Sample size; n = 50

Population standard deviation; σ = 3140

Let's define the hypothesis;

Null hypothesis; μ ≥ 12800

Alternative hypothesis; μ < 12800

The alternative hypothesis is the claim.

Since sample size is greater than 30, we will use z-score test.

Formula for z-score;

z = (x¯ - μ)/(σ/√n)

z = (12499 - 12800)/(3140/√50)

z = -0.678

From online p-value from z-score calculator attached, using z = -0.678 with one tailed hypothesis and significance value of 0.05,we have;

p - value = P(z < -0.678) = 0.2489

The p-value is greater than the significance value, so we will fail to reject the null hypothesis and conclude that there is no sufficient information to support the leasing firm's claim

Answer: [tex]322\ lb[/tex]

Step-by-step explanation:

Given

The magnitude of the force [tex]F=350\ \text{Pounds}[/tex]

The force makes an angle of [tex]67^{\circ}[/tex] with the horizontal

So, the components of the force are

[tex]\Rightarrow F\cos 67^{\circ}, F\sin 67^{\circ}\\\Rightarrow F\cos 67^{\circ}=350\cos 67^{\circ}\\\quad \quad =136.75\ lb\\\text{Similarly, }\\\Rightarrow F\sin 67^{\circ}=350\sin 67^{\circ}\\=322.17\ lb[/tex]

The larger among the two is [tex]F\sin 67^{\circ}[/tex] i.e. [tex]322\ lb[/tex]

Answer: all cones with the same height are always similar. False... radii could differ. ... Doubling the radius of a sphere doubles its surface area.

Step-by-step explanation:

Answer:

a)  c. 90.

b) The margin of error of the point estimate is of 6.19 minutes.

c) The minimum sample size needed to obtain this amount of precision is 289.

Step-by-step explanation:

(a) Which of the following numbers gives the value of the point estimate?

The value of the point estimate is the sample mean, of 90 minutes. So the answer is given by option c.

(b) Using the information given above, calculate the margin of error (in minutes) of the point estimate. Assume we would like to estimate the population mean with 95% confidence.

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0639.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Here, we have [tex]s = 15, n = 25[/tex]. So

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]M = 2.0639\frac{15}{\sqrt{25}}[/tex]

[tex]M = 6.19[/tex]

The margin of error of the point estimate is of 6.19 minutes.

Question c:

College students tend to watch sports between 0 and 120 minutes per day, which means that the standard deviation for population can be estimated as the standard deviation of an uniform distribution with [tex]a = 0, b = 120[/tex]. This standard deviation is:

[tex]\sigma = \sqrt{\frac{(b-a)^2}{12}}[/tex]

Then

[tex]\sigma = \sqrt{\frac{(120-0)^2}{12}}[/tex]

[tex]\sigma = 34.64[/tex]

Minimum sample size:

Now, since we have an estimate for the standard deviation of the population, we use the z-distribution.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The minimum sample size is n for which M = 4. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]4 = 1.96\frac{34.64}{\sqrt{n}}[/tex]

[tex]4\sqrt{n} = 1.96*34.64[/tex]

[tex]\sqrt{n} = \frac{1.96*34.64}{4}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*34.64}{4})^2[/tex]

[tex]n = 288.1[/tex]

Rounding up:

The minimum sample size needed to obtain this amount of precision is 289.

Answer:

About 220 of the students scored less than 96

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.

Mean of 156 and a standard deviation of 23.

This means that [tex]\mu = 156, \sigma = 23[/tex]

Proportion that scored less than 96:

p-value of Z when X = 96. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{96 - 156}{23}[/tex]

[tex]Z = -2.61[/tex]

[tex]Z = -2.61[/tex] has a p-value of 0.00453.

About how many of the students scored less than 96?

0.00453 out of 48592.

0.00453*48592 = 220.1.

Rounding to the closest integer:

About 220 of the students scored less than 96

Answer:

220

Step-by-step explanation:

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