Can anyone explain how to do this?

Answer:  \(\bold{y=-\dfrac{1}{3}x+6}\)

                \(\bold{y=-\dfrac{1}{4}x+\dfrac{25}{4}}\)

Step-by-step explanation:

  x + 3y = 18

- x           -x

        3y = -x + 18

      ÷3     ÷3 ÷3

         y = (-1/3)x + 6

-3x - 12y = -75

+3x           +3x

        -12y = 3x - 75

       ÷-12    ÷-12 ÷-12

           y = (-1/4)x + (25/4)

Answer:

Cost of 1 case of oranges is $ 15 and cost of 1 case of grapefruits is $ 20

(Cost of 1 case of oranges and 1 case of grapefruits altogether equal to \(15+20=\$35\))

Step-by-step explanation:

Let cost of 1 case of oranges be \(\$x\) and cost of 1 case of grapefruits be \(\$y\)

As  cost of 5 cases of oranges and 8 cases of grapefruit is $235,

\(5x+8y=235\)           ...(i)

As  cost of 3 cases of oranges and 2 cases of grapefruit is $85,

\(3x+2y=85\)          ...(ii)

Multiply equation (ii) by \(-4\)

\(-12x-8y=-340\)      ...(iii)

Add (i) and (iii)

\(-7x=235-340\\-7x=-105\\x=\frac{-105}{-7}\\ =15\)

Put \(x=15\) in (i)

\(5(15)+8y=235\\75+8y=235\\8y=235-75\\8y=160\\y=\frac{160}{8}=20\)

So,

Cost of 1 case of oranges is $ 15 and cost of 1 case of grapefruits is $ 20

Therefore,

Cost of 1 case of oranges and 1 case of grapefruits altogether equal to \(15+20=\$35\)

Answer:

-7

Step-by-step explanation:

-2(3x-5)=52

-6x+10=52

-6x=52-10

-6x=42

x=42/-6

x=-7

Answer:

7/64

Step-by-step explanation:

7/6÷8=7/6*1/8=7/64

Hope this helps :)

Answer:

360 in

Step-by-step explanation:

To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:

\(\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}\)

So, the dressmaker has 360 in of ribbon.

Answer:

It may take 20 to 30 seconds.

Step-by-step explanation: Hope this helped

brainliest?

The average time it took for a tablet to dissolve in water that was 22 °C in temperature was 28.3 seconds.

Any substance that, when consumed, alters the physiology or psychology of an organism qualifies as a drug.

The properties of the API (active pharmaceutical ingredient) such as

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If chuck earns additional 40,000 of taxable income, 23.52% the marginal tax rate on this income

Chuck, a single taxpayer, earns $76,000 in taxable income and $1 in interest from an investment in city of heflin bonds.

Tax on $76,000

4,617.5 + (76,000 - 40,125) * 22% = 12,510.0

Taxable income 76,000 + 40,000 = 116,000

Tax on $116,000  

14,605.5 + (116,000 - 85,525) * 24% = 21,919.5

Marginal tax rate

(21,919.5 - 12,510) / 40,000 = 23.52%

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In interval notation, we can represent the largest set of continuity as (-∞, ∞). This means that the function is continuous for all values of x.

To determine the largest set where f is continuous, we need to consider the factors that could cause discontinuity in the function. One possible cause is a vertical asymptote, which occurs when the denominator of a fraction in the function approaches zero. However, since there are no fractions in the given function f(x), we do not need to worry about vertical asymptotes.

Another possible cause of discontinuity is a jump or a hole in the function, which occurs when the function has different values or is undefined at a specific point. To determine if there are any jumps or holes in f(x), we need to find the roots of the function by setting f(x) equal to zero and solving for x:

6x³ + 5x¹ - 2 = 0

We can factor this equation by grouping:

(2x - 1)(3x² + 3x + 2) = 0

Using the quadratic formula to solve for the roots of the second factor, we get:

x = (-3 ± sqrt(3² - 4(3)(2))) / (2(3))

x = (-3 ± sqrt(-15)) / 6

x = (-1 ± i*sqrt(5)) / 2

Since these roots are complex numbers, they do not affect the continuity of the function on the real number line. Therefore, there are no jumps or holes in f(x) and the function is continuous on the entire real number line.

In interval notation, we can represent the largest set of continuity as (-∞, ∞). This means that the function is continuous for all values of x.

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When using a metric ruler with ten equally spaced increments between each labeled centimeter, the length of an object can be recorded to one decimal place.

A metric ruler is typically divided into centimeters (cm) and millimeters (mm). The ruler has ten equally spaced increments between each labeled centimeter, which means that each centimeter can be divided into ten equal parts. Each of these parts represents a millimeter, and they can be used to measure smaller lengths with more precision.

When using a metric ruler to record the length of an object in centimeters, the smallest division on the ruler that can be used to measure the length is a millimeter. The length of the object can be estimated to the nearest millimeter by aligning it with the closest division on the ruler.

To express the length of the object in centimeters, the number of millimeters must be divided by 10. The resulting value will represent the length of the object in centimeters, rounded to the nearest tenth of a centimeter. This means that the length of the object can be recorded to one decimal place.

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Answer: The person above me is correct. Here is a picture if you still dont get it..

Step-by-step explanation:

Since the second derivative is zero at x = -4, the second derivative test is inconclusive.

What are critical values ?

In mathematics, critical values refer to the values of a function where the derivative is zero or undefined. They are important because they can help us identify the maximum and minimum points of a function.

To find the critical values of the function f(x) whose derivative is

2f'(x) =  \((x + 4)^{13}\) we need to solve the equation f'(x) = 0, or equivalently,  \((x + 4)^{13}\) = 0

This equation has only one solution, which is x = -4. Therefore, the critical value of f(x) is x = -4.

To determine whether this critical value is a maximum, minimum, or neither, we need to use the second derivative test. The second derivative of f(x) is given by:

f''(x) = 39\((x + 4)^{12 }\)

Evaluating f''(-4), we get:

f''(-4) = 39(0) = 0

Therefore, Since the second derivative is zero at x = -4, the second derivative test is inconclusive.

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The inversion of the Sackur-Tetrode equation yields the expression for the internal energy U(S, V, N) of an ideal gas. By using the thermodynamic identity, expressions for temperature T, pressure p, and chemical potential µ can be derived. The ideal gas law pV = NkBT is verified through this derivation.

The Sackur-Tetrode equation for the entropy of an ideal gas is:

S = Nk [ ln (V/N (4πmU/3Nh²\()^{3/2}\)) + 5/2 ]

Inverting this equation to obtain U(S, V, N)

U = 3/2 (S/Nk - 5/2 k ln(V/N(4πm/3Nh²\()^{3/2}\))

Next, using the thermodynamic identity U = TdS − pdV + µdN, we can derive expressions for T, p, and µ:

T = (∂U/∂S)|V,N = 3/2 k[(∂S/∂S)|V,N] = 3/2 k

p = - (∂U/∂V)|S,N = NkT/V

µ = (∂U/∂N)|S,V = -5/2 kT ln(V/N(4πm/3Nh²\()^{3/2}\))

Finally, we can verify the ideal gas law pV = NkBT by substituting the expression for T into the expression for p, giving:

pV = NkT/V * V = NkT

which is consistent with pV = NkBT. Thus, we have derived the expression for U(S, V, N), as well as expressions for T, p, and µ, and verified the ideal gas law.

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Answer:

The mean is lower than the median which is lower than the mode.

Step-by-step explanation:

The best predicted value given that a person has an IQ of 91 is 94.03.

Here, we are given that-

sample size n = 20

sample mean for the independent value x = 100.39

sample mean for the dependent value y = 103.6

coefficient of correlation r = 0.925

The general expression for representing a linear model is given by-

y = β₀ + β₁x

where β₀ is the intercept and β₁ is the slope

For the above given case, the linear model will be given as-

y = -3.34 + 1.07x

where -3.34 is the intercept and 1.07 the slope.

To find the best predicted value when X = 91, we substitute the value of x as 91 in the equation as follows-

y = -3.34 + 1.07(91)

y = 94.03

Thus, the best predicted value given that a person has an IQ of 91 is 94.03.

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Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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We accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

We have given: μ = 14, x bar = 16, n = 40, s = 6,  α = 5%, = 0.05

To test μ0 : μ = 14   Vs  H1: μ > 14

Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081

So, P value = 0.021

Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

P value for the hypothesis test

n = 50, x bar = 420, sx = 81, μ = 400,

To test:  H0: μ 400    Vs   H1:  μ > 400

It is right tail test

Test statistics =  (X bar - μx)√n / sx = (420 - 400) √50 / 81 =

z = 1.7459

P value = 0.04093

Declsion: We reject H0 is p value < α

Here α = 0.05

Hence P value < α

Conclusion: We accert H1 alternative that is result is population mean greater than 400.

Hence, we accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

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The requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
From the given data,
Name Number of Cards

Chris      7

Mike       8

Sally       10

Susan     25
Total cards = 50

Now equivalent to Mike’s portion of the total number of cards is given as ,
= Mike cards/total card
= 8 / 50 × 100%
= 4/25×400%
= 16%

Thus, the requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.

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The nurse manager approves two staff nurses to attend a national conference.

The nurse manager has given their authorization or consent for two staff nurses to participate in and attend a national conference. This decision indicates that the nurse manager recognizes the value and relevance of the conference for professional development and sees the benefit of the staff nurses' participation. By approving their attendance, the nurse manager demonstrates support for their growth, learning, and exposure to new knowledge, experiences, and networking opportunities available at the conference.

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The correct option is B: V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy

This integral will give us the Volume of the solid generated when region R is revolved about the vertical line x = 1.

The volume of the solid generated when region R is revolved about the vertical line x = 1, we can use the method of cylindrical shells.

The formula for the volume of a solid generated by revolving a region R about a vertical line is given by:

V = 2π ∫[a,b] x * f(x) dx

In this case, since we are revolving the region R about the vertical line x = 1, the limits of integration will be from y = 2 (where the horizontal line y = 2 intersects the graph y = 2x - 2) to y = 0 (where the graph y = 2x - 2 intersects the x-axis).

Let's analyze the options provided:

A. π ∫[1,2] ((y + 2)/2 - 1)^2 dy

B. π ∫[0,2] ((y + 2)/2 - 1)^2 dy

C. π ∫[1,2] (2 - (2x - 2))^2 dy

D. π ∫[0,2] ((y + 2)/2)^2 - 1^2 dy

Option A: The limits of integration are incorrect. We need to integrate with respect to y, not x.

Option B: This appears to be the correct integral setup, integrating with respect to y and using the correct limits of integration.

Option C: This option incorrectly uses the expression (2 - (2x - 2))^2, which doesn't match the function y = 2x - 2.

Option D: The limits of integration are incorrect. We need to integrate from y = 2 to y = 0.

Therefore, the correct option is B:

V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy

This integral will give us the volume of the solid generated when region R is revolved about the vertical line x = 1.

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Answer:

270 degrees

Step-by-step explanation:

\(Area \: of \: the \: sector \\ \\ = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ 339.3 = \frac{ \theta}{360 \degree} \times 3.14 {(12)}^{2} \\ \\ 339.3 = \frac{ \theta}{360 \degree} \times 3.14 \times 144 \\ \\ \theta = \frac{339.3 \times 360 \degree}{3.14 \times 144} \\ \\ \theta = \frac{122,148\degree}{452.16} \\ \\ \theta= 270.143312 \degree \\ \\ \theta \approx \: 270\degree\)

a) Height at 2, h(2) = 64 feet

b) The rocket will hit the ground 3 seconds after it was launched.

a. To find h(2), we simply substitute t = 2 in the given equation:

h(2) = -16\((2)^{2}\) + 48(2) = 64 feet

This means that 2 seconds after the bottle rocket was launched, it had reached a height of 64 feet.

b. We know that the rocket will hit the ground when its height h(t) equals zero. So, we need to solve the equation:

-16\(t^{2}\) + 48t = 0

We can factor out -16t to get:

-16t(t - 3) = 0

This gives us two possible solutions:

t = 0 (which corresponds to the time when the rocket was launched)

t = 3 (which corresponds to the time when the rocket hits the ground)

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Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

The largest number among the given options is (101001)2, which is option D.

To determine the largest number among the given options, we need to convert each number into its decimal form and compare them.

A. (101001)2 A. (101001)2:

This number is in binary format. To convert it to decimal, we use the place value system. Starting from the rightmost digit, we assign powers of 2 to each bit. The decimal value is calculated by adding up the values of the bits multiplied by their respective powers of 2.

(101001)2 = 12^5 + 02^4 + 12^3 + 02^2 + 02^1 + 12^0

= 32 + 0 + 8 + 0 + 0 + 1

= 41

B. (2B)16 = 216^1 + 1116^0 = 32 + 11 = 43

C. (52)s: The base "s" is not specified, so we cannot determine its decimal value.

D. 50

Comparing the values we obtained:

41 < 43 < 50

Therefore, the largest number among the given options is 50, which corresponds to option D.

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Answer:

9(-9x+3), 27(-3x+1), -27(3x-1)

Step-by-step explanation:

If u calculate everything together u will definitely get your answer of -81x + 27

Answer:

E

Step-by-step explanation:

Have a good day :)

Answer:

Answered Perimeter and Area

Step-by-step explanation:

I am unsure of what you need here but here's 2 possible answers

Area

We can use composite shapes to figure out the area here (splitting one shape into more then adding up their total areas)

This shape has a rectangle with an Area of (24*30mm) but wwith a square cut out (20^2)

If we just solve we get the Area

A = (24*30) - 20^2

A = 720 - 400

A = 320mm^2

Perimeter

Perimeter is also pretty easy since we just add up side lengths.

(30 + (24*2) + (10*2) + (20*3))

(30 + 96 + 20 + 60)

= 206mm

Answer:

\(m=0.02\)

Step-by-step explanation:

\(4.3m=0.086\\m=\frac{0.086}{4.3} \\m=0.02\)

Answer:

x=36

Step-by-step explanation:

5x=180

x=180/5=36

Answer:x=36

Step-by-step explanation:

Took the test and got it right!

Answer:

the first is  1/5 what are the other options

Step-by-step explanation: