Harper and her children went into a bakery and will buy cupcakes and brownies.
Each cupcake costs $4.25 and each brownie costs $2.75. Harper has a total of $40 to
spend on cupcakes and brownies. Write an inequality that would represent the
possible values for the number of cupcakes purchased, c, and the number of brownies
purchased, b.

These values are based on the t-distribution table and represent critical values for the given probabilities and degrees of freedom.

To answer this question, we need to use a t-table. The values we are looking for are the t-values associated with specific probabilities and degrees of freedom.

(a) t0.10, 10 = 1.372 (from the t-table, using 10 degrees of freedom and the probability of 0.10)

(b) t0.05, 10 = 1.812 (from the t-table, using 10 degrees of freedom and the probability of 0.05)

(c) t0.05, 21 = 1.721 (from the t-table, using 21 degrees of freedom and the probability of 0.05)

(d) t0.05, 60 = 1.671 (from the t-table, using 60 degrees of freedom and the probability of 0.05)

(e) t0.005, 60 = 2.660 (from the t-table, using 60 degrees of freedom and the probability of 0.005)

Note that we round all answers to three decimal places, as specified in the question. The values we have found are the t-values for the specified probabilities and degrees of freedom. These values can be used in calculations involving t-distributions.

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Martha collected 11/4 or 2.75 more quarts of berries than Daniel.

To find out how many more quarts of berries Martha collects than Daniel, we need to subtract Daniel's collection from Martha's collection. First, we need to convert Martha's collection to a mixed number if we want to subtract it from Daniel's collection.

5 1/2 quarts can be written as 5 + 1/2 = 10/2 + 1/2 = 11/2 quarts.

Now we can subtract Daniel's collection from Martha's collection:

Martha's collection - Daniel's collection = 11/2 - 4.75

To subtract fractions, we need to have a common denominator. In this case, we can convert 4.75 to a fraction with a denominator of 2:

4.75 = 4 + 0.75 = 4 + 3/4 = 8/2 + 3/4 = 11/4

Now we can subtract:

11/2 - 11/4 = (22/4) - (11/4) = 11/4

Therefore, Martha collected 11/4 or 2.75 more quarts of berries than Daniel.

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Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of phones produced abroad and y represent the number of phones produced locally.

The company can provide 6000 hours of labor each week and it takes 30 hours to produce the cellphone abroad and at the local factory it takes 20 hours, hence:

30x + 20y = 6000            (1)

Also, there is a total resource of $12000 each week, the cost of producing abroad is $20 and the cost of producing locally is $60. Hence:

20x + 60y = 12000           (2)

Multiply equation 1 by 3 and subtract equation 2 from the result. This gives:

70x = 6000

x = 600/7 ≈ 86

Put x = 86 in equation 1:

30(86) + 20 y = 6000

20y = 3420

y = 171

86 phones should be produced abroad and 171 phones locally

We need to  know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.

Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.

Therefore the margin of error is influenced by confidence level and sample size.

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Answer:

yes

Step-by-step explanation:

A proportional equation is of the form

y = kx and the constant of proportionality is k

y = 1.2x  is proportional

The true statement is B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1), by comparing the probabilities and interpreting the likelihood.

From the given information,

Probability of the batting average of player 1 = 4/7

Probability of the batting average of player 2 = 5/8

Probability of the batting average of player 3 = 3/6 = 1/2

We have to find the likelihood of each player.

LCM (7, 8, 6) = 56

Probability of player 1 = (4 × 8) / (7 × 8) = 32/56

Probability of player 2 = (5 × 7) / (8 × 7) = 35/56

Probability of player 1 = (1 × 28 ) / (2 × 28) = 28/56

Here the likelihood is greatest for player 2, then player 1 and the least likelihood is for player 3.

Hence the correct option is B.

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In the given diagram, the value of x is 90°

From the question, we are to determine the value of x

In the given diagram,

Using the linear pair theorem, we can write that

x + 90° = 180°

x = 180° - 90°

x = 90°

Hence, the value of x is 90°

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The measurement that is closest to the value of x, in centimeters, is given as follows:

14.3.

In this problem, we have a right triangle, in which the legs, which are the sides between the angle of 90º, are of 11.9 cm and 7.9 cm.

Then the hypotenuse x, which is the segment connecting both legs, is obtained using the Pythagorean Theorem.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

Then the length of x is calculated as follows:

x² = 11.9² + 7.9²

x = square root of (11.9² + 7.9²)

x = 14.28.

Closest to 14.3, rounding to the nearest tenth, meaning that the third option is correct.  

We suppose that 11.9 cm and 7.9 cm are the measures of the legs.

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length: 20 units

width: 10 units

Answer:

6 (12+8)

Step-by-step explanation:

the word 'times' would indicate the multiplication of 2 numbers

the word 'sum' would indicate the addition of 2 numbers. in this case, 12 + 8 would be placed in parenthesis

hope this helps!! :)

Answer:

2(x-2) ≤ -30

Step-by-step explanation:

2(twice) (x-2)( the difference of a number and 2) ≤ (is at most )-30

The null we are interested in testing here is that the coefficients on age and age^2 are jointly zero. So, we would need to run a restricted version of the regression above where these two variables are omitted and calculate.

Given:

what other regression do you need to run to test the null hypothesis that, holding other factors fixed, age has no effect on sleeping.

The null we are interested in testing here is that the coefficients on age and age^2 are jointly zero.

\(F = R^2_{ur}-R^2_r / q / 1-R^2_{ur} (n-k-1)\)

Therefore the null we are interested in testing here is that the coefficients on age and age^2 are jointly zero. So, we would need to run a restricted version of the regression above where these two variables are omitted and calculate.

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Answer:

Dilate by a scale factor of 0.5 with the origin as the center of dilation.

Rotate 90° clockwise about the origin

Step-by-step explanation:

Polygon ABCD:

Dilate by a scale factor of 0.5 with the origin as the center of dilation (pink polygon on attached diagram).

This means multiply the x and y values of the points by 0.5:

A → (-1, 2)

B → (-4, 1)

C → (-2, 4)

D → (-1, 3)

Rotate 90° clockwise about the origin: (x, y) → (-y, x)

A' = (-2, 1)

B' = (-1, 4)

C' = (-4, 2)

D' = (-3, 1)

So the transformations are:

Answer:

x<16

Step-by-step explanation:

let x be the number

2x8>x

16>x

Answer:

x = 7 (the number of students)

Step-by-step explanation:

let students = x , adults =y

Equation 1: the  total number of them

x+y=25  (25 because there are 5 for free)

Equation 2: the total price of them

2x+5y=104       (student cost 2$, adult cost 5$)

so we have two equations

x+y=25      (by multiply this equation by -2)

so it will be -2x-2y=-50

by adding 2 equations

-2x-2y=-50

2x+5y=104

0+3y = 54   divide both side by 3

y=18      (the number of adults)

by sub. in Equation (x+y=25)

x+18=25

x=25-18

x = 7 (the number of students)

Answer:

-8 and 15

Step-by-step explanation:

yessir

Answer:

15 and -8

Step-by-step explanation:

15 x -8 = -120

15 + -8 = 15 - 8 = 7

Therefore, the approximate dimensions of the rectangle to the nearest tenth of a meter are width = 7.9 m and length = 10.8 m.

Area is a measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²).

Here,

Let's denote the width of the rectangle as "w" in meters. Then, according to the problem statement, the length of the rectangle can be expressed in terms of the width as:

length = 2w - 5

The area of the rectangle is given as 97 square meters, so we can write:

area = length × width

Substituting the expression for length in terms of the width, we get:

area = (2w - 5) × w

Expanding this expression, we get a quadratic equation in standard form:

2w² - 5w - 97 = 0

We can solve this equation using the quadratic formula:

w = (-(-5) ± √((-5)² - 4×2×(-97))) / (2×2)

Simplifying this expression, we get:

w ≈ 7.9 or w ≈ -6.2

Since the width of a rectangle cannot be negative, we discard the negative solution and approximate the width to the nearest tenth of a meter:

w ≈ 7.9 m

Using the expression for the length in terms of the width, we can find the length:

length = 2w - 5

≈ 10.8 m

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Answer:

Step-by-step explanation:

To solve for the variable n in the equation 1/3 = n + 3/4, you can follow these steps:

Subtract 3/4 from both sides of the equation to isolate the variable n on one side:

1/3 - 3/4 = n

Find a common denominator for 1/3 and 3/4, which is 12. Multiply the numerator and denominator of 1/3 by 4 to get 4/12, and multiply the numerator and denominator of 3/4 by 3 to get 9/12:

4/12 - 9/12 = n

Simplify the expression on the left side of the equation by subtracting the numerators:

-5/12 = n

Rewrite the solution as a fraction or mixed number in simplest form:

n = -5/12

Therefore, the solution to the equation 1/3 = n + 3/4 is n = -5/12.

If \(y=x^m\) is a solution to the ODE

\(x^2 y'' - 7xy' + 15y = 0\)

then substituting \(y\) and its derivatives

\(y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}\)

gives

\(m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0\)

\(m(m-1)x^{m} - 7mx^{m} + 15x^m = 0\)

\((m(m-1) - 7m + 15)x^{m} = 0\)

We ignore the trivial case of \(y=x^m=0\). Solve for \(m\).

\(m(m-1) - 7m + 15 = 0\)

\(m^2 - 8m + 15 = 0\)

\((m - 3) (m - 5) = 0\)

\(\implies \boxed{m=3} \text{ or } \boxed{m=5}\)

The diameter of the given circle with a circumference of 28.6 centimeters is approximately 9.11 cm.

The circumference of a circle is given by the simple formula: C = πd, where C is the circumference, π is the constant pi and d is the diameter of the circle.

Given that the circumference of the circle is 28.6 cm, we can use the formula to find the diameter:

28.6 = πd

d = 28.6/π

Using 3.14 as an approximation for π, we get:

d ≈ 28.6/3.14 ≈ 9.11

Therefore, the diameter of the circle is approximately 9.11 cm.

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Nitrogen gas with a mass of 50.0 g at 2.0 atm and 65 °C will occupy a volume of approximately 25 L.

The Ideal gas law or general gas equation is expressed as:

PV = nRT

Where P is pressure, V is volume, n is the amount of substance, T is temperature and R is the ideal gas constant ( 0.0821 Latm/molK )

Given that:

Mass of the Nitrogen gas m = 50.0 g

Pressure P = 2.0 atm

Temperature T = 65 °C = (65 + 273.15) = 338.15K

Amount of gas n = ?

Volume of gas V = ?

First, we determine the amount of nitrogen gas.

Note: Molar mass of Nitrogen = 28 g/mol

Hence

Number of moles of nitrogen gas (n) = mass / molar mass

n = 50.0g / 28g/mol

n = 25/14 mol

Substituting the values into the ideal gas law equation:

PV = nRT

V = nRT/P

V = ( 25/14 × 0.0821 × 338.15 ) / 2.0

V = 24.78 L

V = 25 L

Therefore, the volume of the gas is 25 L.

Option D) 25 L is the correct answer.

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The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:

Then to find the mass we just multiply the weight in pounds by 0.45:

Therefore the other person has a mass of 45 kg.

The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:

Then to find the mass we just multiply the weight in pounds by 0.45:

Therefore the other person has a mass of 45 kg.

The Steady-state gain can be found using the formula Kp = lim s->0 G(s).

A. (a) The inverse Laplace transform of the function 8 /s² (s+2) is given by f(t) = 8(t - e^(-2t)).

B. (a) To find the inverse Laplace transform of 8 /s² (s+2), we can use partial fraction decomposition and inverse Laplace transform tables.

First, we express the function in partial fraction form as follows: 8 /s² (s+2) = A/s + B/s² + C/(s+2).

To find the values of A, B, and C, we can equate the coefficients of corresponding powers of s in the numerator and denominator. This leads to the equations A + 2B + 2C = 0, A = 8, and B = -8.

Substituting the values of A and B into the equation A + 2B + 2C = 0, we find C = 4.

Now, we have the partial fraction decomposition as: 8 /s² (s+2) = 8/s - 8/s² + 4/(s+2).

Using inverse Laplace transform tables, we find the inverse Laplace transforms of each term: L⁻¹{8/s} = 8, L⁻¹{8/s²} = 8t, and L⁻¹{4/(s+2)} = 4e^(-2t).

Finally, we combine the inverse Laplace transforms of each term to obtain the inverse Laplace transform of the original function: f(t) = 8(t - e^(-2t)).

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Answer:

Wrong order!

Step-by-step explanation:

There's a reason why coordinates are called an "ordered pair", and for every point (a, b) a is the x coordinate and b is the y coordinate. The calculations are correct, the way reporting them are not: the point should be (3.0) and (0,2) - in fact, all points on the x axis are of the form (p, 0) and all points on the y axis of the form (0,q)

The main advantage of an independent measures design is that it reduces the risk of order or practice effects and minimizes the influence of individual differences between participant

An independent measures design, also known as a between-subjects design, is a type of research study in which different groups of participants are used for each condition being tested.

In other words, each participant is only exposed to one condition, and the data from each group is analyzed and compared to determine if there are any significant differences between the groups.

The main characteristics of an independent measures design are:

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Answer:

\($\frac{5\sqrt{2} }{2}$\)

Step-by-step explanation:

\(x: \text{opposite side of the angle of 45\º}\)

\(5: \text{hypotenuse of the right triangle}\)

\($\sin(\theta)=\frac{\text{opp}}{\text{hyp}} \Rightarrow \sin(45\º)=\frac{x}{5} $\)

\($\text{Once }\sin(45\º)=\frac{\sqrt{2} }{2} $\)

\($\frac{\sqrt{2} }{2} =\frac{x}{5} \Rightarrow 2x=5\sqrt{2} \Rightarrow x=\frac{5\sqrt{2} }{2} $\)

You can just remember that 5 is the diagonal of a square of side length x.

\($5=x\sqrt{2} \Rightarrow x=\frac{5}{\sqrt{2} } \Rightarrow x=\frac{5}{\sqrt{2} } \cdot \frac{\sqrt{2} }{\sqrt{2} } = \frac{5\sqrt{2} }{2} $\)

Answer: C and D

Step-by-step explanation:

∠AFD measures 150°, not 130° and ∠AFB & ∠CFD are complementary, not supplementary.

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ - 9 \: , \: - 5 \: , - 1 \: , \: 3 \: }}}}}\)

Option C is the correct option.

Step-by-step explanation:

Here, y = 2x - 5 and domain ( D ) = { -2 , 0 , 2 , 4 )

when, x = -2 , Range = 2 × (- 2)- 5 = - 4 - 5 = -9

when, x = 0 , range = 2 × 0 - 5 = 0 - 5 = -5

when x = 2 , range = 2 × 2 - 5 = 4 - 5 = -1

when, x = 4 , range = 2 × 4 - 5 = 8 - 5 = 3

Range = { -9 , -5 , -1 , 3 }

Hope I helped!

Best regards! :D

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

did test got it right

Answer:

pretty sure its B

Step-by-step explanation: