1. Eli and Amy brought in 3 packs of stickers to give out to their two classes. They had enough for Mrs. O's 21 students, Mrs. L's 24 students and even had 15 stickers left over! How many stickers were in 1 each pack?
2. Teo is inviting 9 boys and 4 girls to his birthday party. He has a package of 28 candies. He wants to give the same number of candies to each of his party guests and himself. How many candies will each 2 guest get?
3. The pet store got 6 boxes of new dog collars. There were 4 collars in each box. Blanca unpacked them 3 all and hung them up in 3 equal rows on the wall. How many collars were in each row?
4. Scout leader Jill has 2 troops. Her first grade troop has 9 girls who each earned 7 badges. Her second grade troop has 12 girls who each earned 5 badges. How many more badges did the first graders earn 4 than the second graders?
5. Sophie has a $20 bill. She buys 3 keychains that each cost $4. How much money does Sophie have 5 left?
6. Jenny is making bracelets. Each bracelet uses 9 inches of string. She has 3 packages of string that 6 are each 36 inches long. How many bracelets can she make?
7. Carson wants to rent a boat. The boat costs $50 an hour to rent and he wants to rent it for 2 and a half 7 hours. Carson already has $90 saved up. How much more does he need to save?
8. Jesse sold 12 hot dogs and 9 popcorns while working at the snack stand. Each hot dog costs $2 and 8 popcorn costs $1. How much money did she take in altogether?​

Answer:

Below

Step-by-step explanation:

1/3 x   = - 2/5      <=====multiply both sides of the equation by 3 to get

x = -6/5   = - 1  1/5

The total income from the machines over the first 5 years is $185.89

From the question, we have the following parameters that can be used in our computation:

f(t) = 160e0.03t

Where

Rewrite the function properly

so, we have the following representation

f(t) = 160e⁰.⁰³ⁿ

The above function is an exponential function

So: In the first 5 years, we have the value of t to be 5

This is represented as follows

t = 5

Substitute the known values in the above equation, so, we have the following representation

f(5) = 160e⁰.⁰³ ˣ ⁵

Evaluate the product of the exponents

f(5) = 160e⁰.¹⁵

The products above give

f(5) = 185.89

Hence, the total income is $185.89

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The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.

A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.

The expression for the volume of a regular pentagon is given as V =  5/2 × abh

Where h is the height and a and b are the length of the sides.

Now, the value of a, b and h as per the question is given as,

a = b = h = 1.

Then, the volume can be calculated as,

V = 5/2 × 1 ×1 × 1
   = 2.5

Hence, the volume of the regular pentagonal prism  is given as 2.5 cm³.

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a) The test statistic for the two independent samples is 0.7

b) The p-value for the test sample is 0.483 , here p-value is greater than significance level.Thus, there is no sufficient evidence to reject null hypothesis.

Given,

significance level, \alpha = 0.04

From population 1,

Mean, [tex]x_1=13.2[/tex]

variance, [tex]\sigma^2_1=39[/tex]

standard deviation, [tex]\sigma_1 =6.24[/tex]

sample size,[tex]n_1=62[/tex]

From population 2,

Mean, [tex]x_2=11.5[/tex]

variance, [tex]\sigma^2_2 = 29[/tex]

standard deviation, [tex]\sigma_2=4.47[/tex]

Test hypothesis,

[tex]H_0:(\mu_1-\mu_2)=1.6\\\\H_a:(\mu_1-\mu_2)\neq1.6[/tex]

a)

The test statistic can be determined by formula,

[tex]z=\frac{(x_1-x_2)-d}{\sqrt{\frac{S^2_1}{n^2_1}+\frac{S^2_2}{n_2}}}[/tex]

[tex]d=\mu_1-\mu_2=1.6[/tex]

[tex]z=\frac{(13.2-11.5)-1.6}{\sqrt{\frac{6.24^2}{62^2}+\frac{4.47^2}{51}}}\\\\z=\frac{0.1}{\sqrt{0.01+0.007}}\\\\z=\frac{0.1}{0.13}=0.7[/tex]

b)

P-value can be calculated by the z-score table

as z=0.7 then from z-value table

p=0.483

A p-value greater than 0.04 (> 0.04) indicates strong support for the null hypothesis. This means that the null hypothesis is retained and the alternative hypothesis is rejected. It is important to note that you cannot accept the null hypothesis; we can only reject it or fail to reject it.

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Answer:

[tex] \sqrt{176} [/tex]

[tex] \sqrt{16 + 11} [/tex]

[tex]4 \sqrt{11} [/tex]

Step-by-step explanation:

The answer is

[tex]4 \sqrt{11} [/tex]

We

need to express 176 as the product of its prime factors i.e. 176 = 2 × 2 × 2 × 2 × 11. Therefore, √176 = √2 × 2 × 2 × 2 × 11 = 4 √11 . Thus, the square root of 176 in the lowest radical form is 4 √11.

i hope this helped

Given:

f(x) = x³ -4x² -3x + 12

     = x² (x -4 ) - 3 (x - 4 )

     = ( x² -3 ) (x-4 )

To find zeros above equation should be equel to zero

x² - 3 = 0 or x - 4 = 0

x² = 3  or x = 4

x = ±√3 or x = 4

The zeros of the given equation are :

x =  ±√3 , x = 4

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In simple linear regression, the p-values for the f test and for the t test are identical since there F test and the t test may or may not yield the same conclusion.

The p-value for a t-test on a single variable and the p-value for an F-test on the entire model will be the same if there is only one variable in the model. When there are multiple variables, the situation changes.

An F-test in regression often evaluates how well several linear models fit each other. The F-test can evaluate many regression coefficients at once in contrast to t-tests, which can only evaluate one regression coefficient at a time.

A tiny p value indicates that all of your results are significant, but a large f value (one that is greater than the F crucial value shown in a table) indicates that something is significant. Simply put, the F statistic contrasts the combined effects of all the factors.

The p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data. The t-value is a way to measure the difference between population means.

F and t tests are needed to test for regression. You must look in the f table to determine the p values for the f test. The degrees of freedom listed in the ANOVA table should be used (provided as part of the SPSS regression output). You must use the Df2 or df denominator to determine the p values for the t test.

Therefore,

In simple linear regression, the p-values for the f test and for the t test are identical since there F test and the t test may or may not yield the same conclusion.

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Sandra needs 8 bowls to divide the trail mix equally.

To determine the number of bowls Sandra needs, we need to divide the total weight of the trail mix by the weight of each bowl.

First, we need to convert the weight of the trail mix from pounds to ounces. There are 16 ounces in a pound, so 5.2 pounds is equal to 5.2 x 16 = 83.2 ounces.

Next, we need to convert the weight of each bowl from pounds to ounces. There are 16 ounces in a pound, so 0.65 pounds is equal to 0.65 x 16 = 10.4 ounces.

Now that we have both weights in the same units, we can divide the total weight of the trail mix by the weight of each bowl to find the number of bowls needed.

⇒ 83.2 ounces / 10.4 ounces per bowl

Apply the division operation,

⇒ 8 bowls.

Therefore, she needs 8 bowls to divide the trail mix equally.

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The scientific terms for peaks and valleys is B. Crests and troughs.

The greatest amount of upward displacement within a cycle occurs at a wave's crest point. A surface wave's crest is a region where the medium's displacement is greatest. The minimum or lowest point in a cycle, a trough is the opposite of a crest.

The crest and trough of a wave, respectively, are its highest and lowest surface portions. The wave height is the vertical distance between the crest and trough. The wavelength is the horizontal separation between two adjacent crests or troughs.

The crest is the highest point on the wave. The trough is the area that is the lowest. The wave length, also known as the wavelength, is the separation between two successive crests (or troughs), while the wave height is the overall vertical change in height between the crest and the trough.

Therefore, based on the information given, the correct option is B.

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Answer: 160 inches

Step-by-step explanation:

To put lights around the window, you will need a total of 32 + 48 + 32 + 48 = <<32+48+32+48=160>>160 inches of lights. You will need this much light to go completely around the window.

f(x) = x^3 - 6x^2 + 12x the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. The critical value that will give you a relative maximum is x = 4. The critical value that will give you a relative minimum is x = -2.

The derivative of the given function is f'(x) = 3x^2 - 12x + 12. Setting this equal to 0 gives us x = 0 and x = 4. By the first derivative test, we can determine that the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. Therefore, the critical value that will give us a relative maximum is x = 4 and the critical value that will give us a relative minimum is x = -2. This can be verified by finding the second derivative of the function, which is f''(x) = 6x -12. Setting this equal to 0 gives us x = 2, which is between the two critical values. Since the second derivative is negative for x < 2, the critical value at x = -2 will give us a relative minimum and since it is positive for x > 2, the critical value at x = 4 will give us a relative maximum.

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The correct interpretation for the statement D'(10) = 3 is (e) On January 3, the day length increased by 10 minutes

From the question, we have the following parameters that can be used in our computation:

The function D represents the day length, in minutes, of the nth day of the year in Juneau, Alaska.

This means that

D = minutes

n = days

So, we have

Notation = D(n)

Also, from the question, we have

D'(10) = 3

This is the inverse of the function D(n)

So, the values of the parameters are

D(n) = 10

n = 3

This means that the number of days is 3 and the minute is 10

Hence, the interpretation of D'(10) = 3 is (e)On January 3, the day length increased by 10 minutes

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Step-by-step explanation:

similar means that they have the same angles, and that there is one and the same scale factor for all corresponding sides and other lines (like heights).

so, either the angle F = 60° (like angle C in ABC), or DE has the same scaling factor with AB as DF has with AC.

some correct answer options are not listed, so we need to adjust to the existing ones.

remember, the sum of all angles in a triangle is always 180°.

so,

angle A + angle B + angle C = 180

40 + angle B + 60 = 180

angle B = 80°

so, angle E = 80° for the triangles to be similar.

AC × c = DF

12 × c = 16

3 × c = 4

c = 4/3

so,

AB × c = DE

9 × 4/3 = DE

36/3 = DE

DE = 12

so, either angle E = 80° or DE = 12.

A 90% confidence interval for proportion p ( for registered voters that would vote to raise taxes) = 0.483 is 0.483 +/- 0.024... So, the correct answer is option (b).

We have provide a random sample of 1200 registered voters and found that 580 would vote to raise taxes.

Sample size , n = 1200

The number of voters rise the tax = 580

Let p represent the proportion of registered voters in the state that would vote to raise taxes. From reading the provide data we get ,

sample proportion p = 580/1200 = 29/60 = 0.483

To use the standard error, we replace the unknown parameter p with the p-cap statistic , so p-cap = 0.483

Standard error = √p-cap (1 - p-cap )/n

= √0.483(1- 0.483)/1200 =√0.483(0.517)/1200

=√0.0002080925

= 0.0144254116

Now, the 90% confidence interval for p is

p-cap +/- z√(p-cap(1 - p-cap)/n)

Using the Z-table, z-value for 90% confidence interval is 1.645...

So, p-cap +/- z√((1 - p-cap )/n) = 0.483 +/- (1.645)0.014425

= 0.483 +/- 0.023729125 ~ 0.483 +/- 0.024

Hence, the required interval is 0.483 +/- 0.024.

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Answer:

you cannot

Step-by-step explanation:

you cannot graph something like that, it is not a equation of a line nor a point or if you want to solve it it is x = -10

Answer:

Step-by-step explanation:

given in the question that 5x=-50

     on solving the equation

          we get, x=-10

on the graph on the negative x-axis locate the point x=-10

By graphing, the solution to the system, y = 5x + 2 and y = x - 2 is: A. (-1, -3)

The solution to a system of equations is the coordinates of an ordered pair that will make both of the equations to be true. This coordinates is determined by graphing.

To do this, plot both lines on a coordinate plane, then determine the coordinates of the point of intersection of both lines.

Given the system of equations,

y = 5x + 2

y = x - 2

The graph that shows both equations are attached below where the red line is y = 5x + 2, and y = x - 2 is the blue line.

The point of intersection is at (-1, -3). Therefore, the solution is:

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The procedure is correct is  1 + tan²(theta) = sec²(theta)

What is  Fraction?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

And

cos²(theta) = 1 - sin²(theta)

Are both valid identities

Keisha and the David.

As per the question Kisha and the David found the same value of the cosine theta as given by the  Sine theta = Negative Start Fraction 8 Over 17 End Fraction. The Keisha solution and the Davis solution for the solution were tan-squared (theta) + 1 = sec-squared (theta).

Thus the answer is both procedures are correct.

As they both wanted to find the solutions to the numerical problems they made two different methods.

Such as the Sine theta = Negative Start Fraction and the tan-squared (theta) + 1 = sec-squared (theta).

Hence both options are the same and true.

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The maximum no. of fish tacos they can order is 8.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

let, The no. of fish taco be 'F'.

Therefore, 2F + 3.75 ≤ 20.  

So, The no. of fish tacos they order is,

2F ≤ 20 - 3.75.

2F ≤ 16.25.

F ≤ 16.25/2.

F ≤ 8.125 Or 8 as the no. of fish tacos must be in integers.

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The population standard deviation [tex]\sigma[/tex] is 6.697.

The average distance between each data item and the mean is known as the mean absolute deviation.

The gap between each data value and the mean in absolute terms is represented by this average.

The given data set can be arranged as 4, 7, 8, 10, 12, 12, 15, 18, 23, 26.

Mean[tex](\overline{x})[/tex] = (4 + 7 + 8 + 10 + 12 + 12 + 15 + 18 + 23 + 26)/10.

Mean[tex](\overline{x})[/tex] = 135/10 = 13.5.

We know variance[tex](\sigma)[/tex] = [tex](\[ \sum_{i=1}^{n}x_i^2 \]/n) - \overline{x}^2[/tex].

= (4² + 7² + 8² + 10² + 12² + 12² + 15² + 18² + 23² + 26²)/10 - (13.5)².

= (16 + 49 + 64 + 100 + 144 + 144 + 225 + 324 + 529 + 676)/10 - 182.25.

= 44.85

And we also know the standard deviation is [tex]\sqrt{\sigma}[/tex] = [tex]\sqrt{44.85}[/tex] = 6.697

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Answer:B

Step-by-step explanation:

I took the test

Answer:

x = - 3

Step-by-step explanation:

2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify

2x - 12 + 2 = 4x - 4

2x - 10 = 4x - 4 ( subtract 4x from both sides )

- 2x - 10 = 4x - 4 ( add 10 to both sides )

- 2x = 6 ( divide both sides by - 2 )

x = - 3

Answer:

SOLUTION

2(X-6)+2=4X-4

open the blanket by multiplication

2x-12+2=4x-4

2x-10=4x-4

collect like term

2x+4x=-4+10

6x=6

divide both side by 6

x=1

F0.05 (4,5)=5.19>f according to the F-distribution table. Following that, P(F>1.442)>P(F>f0.05 (94.5))=0.05. This leads us to conclude that the sample has a higher than 5% chance of producing such data under the premise that σx=σy.

We cannot conclude that the variances of the two populations are not equal based on the standards of a 95% confidence interval.

Step 1 : the mines' 1 and 2 standard deviations should be calculated. [tex]n_{x}[/tex] =5&[tex]n_{y}[/tex]=6.

To determine the sample means, use the formulas

x bar = 8260 + 8130 + 8350 + 8070 + 8340/ [tex]n_{x}[/tex]

x bar = 41150/ 5

x bar = 8230 and y bar = 7950 + 7890 + 7900 + 8140 + 7920 + 7840/ [tex]n_{y}[/tex]

y bar = 47640/6

y bar = 7940.

step 2: Now,  [tex]s_{x}[/tex]provides the standard deviations.

[tex]s_{x}^{2}[/tex] =1/4i=1∑^5i=1(xi−x)^2

=1/ 4 ⋅63000

=15750

for [tex]s^{2}_{y}[/tex]

[tex]s^{2}_{y}[/tex]^2=1/5∑i=1^6(yi−y)^2

=1/5⋅54600

=10920

If we assume that the variances of the two populations are equal—

that is,  σx=σy and

 [tex]s_{x}^{2}[/tex] and[tex]s^{2}_{y}[/tex] are the variances of independent random samples with sizes of [tex]n_{x}[/tex]=5 and[tex]n_{y}[/tex] =6 drawn from normal populations—then we can say that the random variable exists.

The formula F is

=[tex]s_{x}^{2}[/tex]/ [tex]s^{2}_{y}[/tex]has an F distribution with

v1=nx- 1

=5- 1

=4 and

v2=ny-1

=6- 1

=5

The observed samples' f-value is f=[tex]s_{x}^{2}[/tex] / [tex]s^{2}_{y}[/tex]

=15750/10920

=1.442.

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The correct matching regarding the linear functions are given as follows:

i. A set of points where the coordinates of each point has a sum of 2: Line n.

ii. A set of points where the y-coordinate of each point is 10 less than the x-coordinate: Line m.

b - i) Two numbers with a sum of 2: A and C.

b - ii) Two numbers where the y-coordinate is 10 less than the x-coordinate: D and E.

b - iii) Two numbers with a sum of 2 and where the y-coordinate is 10 less than the x-coordinate: B.

The set of points where the coordinates of each point has a sum of 2 is defined by the following linear function

x + y = 2.

In slope-intercept form, it is of:

y = 2 - x.

Which is the decreasing line n, with an intercept of 2.

A set of points where the y-coordinate of each point is 10 less than the x-coordinate is defined by the following linear function

y = x - 10.

Which is the increasing line m, which an intercept of m.

The coordinates of each point are given as follows:

These points are then used to match the sentences in item b.

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Answer:

It is a reciprocal function

Step-by-step explanation:

f(x) = x, the reciprocal function is f(x) = 1/x

Answer:

The price of a 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, bought to yield 8% convertible semiannually, is its present value of $115.87.

The price of a bond is its present value.

The present value can be computed by setting the following parameters:

This can be done using an online finance calculator with the results as follows:

N (# of periods) = 20 semiannual periods (10 years x 2)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $5 ($100 x 10% x 1/2)

FV (Future Value) = $105

Results:

Present Value (PV) = $115.87

Sum of all periodic payments = $100 ($5 x 20)

Total Interest = $89.13

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Answer: 115.87 (If you don't get this answer then the solution is incorrect.)

(a) Using y the manufacture can find the required diameter of the hole.

(b) The mean of the random variable y is 0.003.

(c) The standard deviation of the y is 0.0063.

(d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

(e)  We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

Given that x1 be the peg diameter with mean 0.25 in. and standard deviation 0.0006 in.and x2 be the hole diameter with mean 0.253in. and deviation 0.002 in.

a) y=x2-x1 denote the difference between hole and peg diameter

if y<0 , the peg won’t go inside the hole and

if y>0 ,the peg be loose to the hole

So using y the manufacture can find the required diameter of the hole.

b)Now, we have to find the mean of the random variable y

μ(y) = μ(x2) - μ(x1)

μ(y) = 0.253-0.25

μ(y) = 0.003

c) Now we have to find the standard deviation of the y

σ(y) = √{var(x1)+ var(x2)}(x1 and x2 are independent)

σ(y) = √0.000036+0.000004

σ(y) = √0.00004

σ(y) = 0.0063

d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

e) With a standard deviation larger than the mean , it would be fairly likely to observe a negative value of y, so it would be a relatively common occurrence to find a peg that was too big to fit in the predrilled hole. We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

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The degree to turn before walking 673 paces is 59 degrees

From the question, we have the following parameters that can be used in our computation:

Lengths = 989 paces, 673 paces and 861 paces

These paces can be represented as

x = 989

y = 673

z = 861

The measure of the required angle (angle Z) i.e.  the degree to walk can be calculated using the following cosine rule

z² = x² + y² - 2xy * cos(Z)

Substitute the known values in the above equation, so, we have the following representation

861² = 989² + 673² - 2 * 989 * 673 * cos(Z)

Evaluate the exponents, the products and the summation

So, we have the following representation

741321 = 1431050 - 1331194 * cos(Z)

Evaluate the like terms

- 1331194 * cos(Z) = -689729

Divide both sides by  - 1331194

cos(Z) = 0.51812808651

Take the arc-cos of both sides

Z = 58.7

Approximate

Z= 59 degrees

Hence, the measure of the angle is 59 degrees

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Answer: She needs to ride 13.9 more kilometers on her bike to finish the race.

Step-by-step explanation:

==> 30 = 3.75 + 12.35 + x

Take 16.1 from both sides:

==> 30 = 16.1 + x

==> 30 = 13.9km

Answer:

Step-by-step explanation:

The answer would be 13.9, if you add 12.35 to 3.75 you get 16.1, then 16.1 added to 13.9 equals 30