You are the new owner of a music shop in Vincennes. The previous owner fled the cityto join the circus as a magician . Your first duty as new owner and store manager is tocreate an advertising plan based on the budget available. You must figure out how manymagazine and TV ads to purchase.TV ads cost $600 per airing.Magazine ads cost $1200 perissue.You total advertising budget is $9,000.1. If we let x = TV ads and y = magazine ads, write an inequality for our advertisingbudget constraint.book bog £9,0002. Due to space limitations, the magazine publishers tell us that we are only allowedto purchase up to 6 magazine ads. Write an inequality for this constraint.3. The television station called to say that we are only allowed to purchase up to 7TV ads. Write an inequality for this constraint.

Answer:

5/14

Step-by-step explanation:

(5/4)(7/2)

Multiply the numerators with the denominators.

5*2=10

4*7=28

10/28 = 5/14

A jet leaves a runway whose bearing is N 35°E from the control tower. After flying 4 miles, the jet turns 90° and flies on a bearing of S 55° E for 5 miles the bearing of the jet from the control tower is mathematically given as

N76.675E

Generally, the equation for horizontal distance is mathematically given as

sin<AOC=\frac{AC}{OA}

Therefore

sin <AOC=\frac{AC}{5}

AC=4

and

BE=3.6

Total horizontal distance=4+3.6

Total horizontal distance=7.6

For Total vertical distance

cos<AOC=OC/OA

cos<AOC=OC/5

OC=3

and

A.E=4.8

Total vertical distance=3-4.8

Total vertical distance=-1.3=E.C=y

In conclusion, the angle

\(\theta=tan{-1} \frac{-1.3}{7.6}\)

\(\theta= -13.324\)

Hence

90-13.324=N76.675E

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Answer:

Step-by-step explanation:

1. Get mileage per gallon by dividing miles traveled by gallons used

\(\frac{125}{5} = 25 mpg\\\)

2. Divide miles you want to travel by the mileage per gallon you got on the first step

\(\frac{400}{25} = 16 gallons\)

Answer: is 4:2 ratio and 3:5

-3,5 is negative and 2,4 positive

Step-by-step explanation:

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Skipper's finance charge at the end of the billing period is given as follows:

$14.77.

The finance charge is obtained using simple interest, as there is a simple compounding per year for the debt, and the charge is the amount of interest accrued during the period of one month.

The amount of interest accrued after t years, using simple interest, is given as follows:

I(t) = Prt.

The parameters for the equation are given as follows:

Considering a period of one month = 1/12 of an year, the values of these parameters for this problem are given as follows:

P = 933, r = 0.19, t = 1/12.

Hence the finance charge for Skipper's purchase is calculated as follows:

I = 933 x 0.19 x 1/12 = $14.77.

(rounding to the nearest penny = nearest cent).

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Answer:

4.6666(repeating)

Step-by-step explanation:

The  circle is:\(x^2+y^2 = 5^2 = 25\)This circle has center (0,0) and radius 5 units. Therefore, it is a circle with a radius of 5 units, and every point that lies on the circumference of this circle is 5 units away from the center of the circle.

the distance between any point on the circle and the center of the circle is always 5 units. This is because the equation of a circle is

\((x-a)^2+(y-b)^2=r^2\)

where the center is (a,b) and the radius is r units. In this case,

a=b=0 and r=5.

Algebraically show that the point (6, 8) lies on the circle.

To show that the point (6, 8) lies on the circle, we need to substitute the values of x and y in the equation of the circle and verify whether the equation holds true or not.So,

substituting x=6 and y=8 in the equation of the circle, we

\(get:6^2 + 8^2 = 36 + 64 = 100\)

Now, we can see that the LHS of the equation is equal to 100, which is also equal to the square of the radius of the circle. Therefore, the point (6, 8) lies on the circumference of the circle with center (0,0) and radius 5 units.

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Answer:

c. 0.778 < p < 0.883.

Step-by-step explanation:

The formula for confidence interval for proportion =

p ± z score × √p(1 - p)/n

p = x/n

n = 195, x = 162

z score for 95% confidence Interval = 1.96

p = 162/195

p = 0.8307692308

p ≈ approximately equal to = 0.8308

0.8308 ± 1.96 × √0.8308 × (1 - 0.8308)/195

0.8308 ± 1.96 ×√0.8308 × 0.1692/195

0.8308 ± 1.96 × √0.0007208788

0.8308 ± 1.96 × 0.0268491862

0.8308 ± 0.052624405

Confidence Interval

= 0.8308 - 0.052624405

= 0.778175595

Approximately = 0.778

= 0.8308 + 0.052624405

= 0.883424405

Approximately = p

0.883

Therefore, the confidence interval for this proportion = (0.778, 0.883) or option c. 0.778 < p < 0.883

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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(a) The value of the z-score for the 6.4 fluid ounce orange is -1.64

(b) The value of the z-score for the 3.11 fluid ounce orange is -4.63

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

Mean = 8.2

Standard deviation = 1.1

The values of the z-scores is calculated as

z = (z - Mean)/Standard deviation

So, we have

z = (z - 8.2)/1.1

When the score is 6.4, we have

z = (6.4 - 8.2)/1.1

Evaluate

z = -1.64

Recall that

z = (z - Mean)/Standard deviation

So when the score is 3.11, we have

z = (3.11 - 8.2)/1.1

Evaluate the expression

z = -4.63

Hence, the values of the z-scores are -1.64 and -4.63

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As n = 4, and we want to know the probability of the 4 being heads, there is only one possible outcome that gives this result:

Answer:

Answer:

56.7°

Step-by-step explanation:

A rectangle is 5.1 cm wide and each diagonal is 9.3 cm long. What is the measure of the angle between a diagonal and the shorter side of the rectangle to the nearest tenth of a degree?

We solve this question using the Trigonometric function of Sine

From the question, we are told that:

A rectangle is 5.1 cm wide

and each diagonal is 9.3 cm long.

Since we have a diagonal, this means the shape is transformed to a triangle.

The width of the rectangle = Adjacent side of a triangle = 5.1cm

The diagonal of the rectangle = Hypotenuse = 9.3cm

Hence,

cosθ = Adjacent/Hypotenuse

cosθ = 5.1/9.3

cosθ = 0.5483870968

θ = arccos(0.5483870968)

θ = 56.743568714°

Approximately = 56.7°

The measure of the angle is 56.7°

Answer:

1.) inverse proportion : 1kx = y

2) direct proportion. y = kx

Answer:

-4 ; -1 ; 2 ; 5

Step-by-step explanation:

-4 is smaller because when counting from zero to the left it is descending but ascending numerically. 0 to -1 to -2 to -3 etc

After that you write the next numbers in ascending order

Answer:

C. \( y = -\frac{1}{2}x - \frac{7}{2} \)

Step-by-step explanation:

We can get the equation in slope-intercept form if we know the slope (m) and the y-intercept (b).

Since the line is parallel to -2x + 4y = 8, it will have the same slope as the equation.

Converting -2x + 4y = 8 into the slope-intercept form, we would have:

4y = -2x + 8

y = -2x/4 + 8/4

y = -½x + 2

Theregore, slope, m, of the line that is parallel bro 4y = -2x + 8 is -½.

To find the y-intercept, b, substitute (x, y) = (-5, -1) and m = -½ in y = mx + b.

Thus:

-1 = (-½)(-5) + b

-1 = ⁵/2 + b

-1 - ⁵/2 = b

(-2 - 5)/2 = b

-⁷/2 = b

b = -⁷/2

To get the equation of the line, substitute b = -⁷/2, and m = -½ in y = mx + b.

The equation would be:

\( y = -\frac{1}{2}x - \frac{7}{2} \)

Answer:

11.7 hours

Step-by-step explanation:

According to data gathered between the years of 2015-2020 from full-time University Students at various Universities throughout the US, it was discovered that they spend roughly 11.7 hours completing these tasks (sleeping, grooming, eating/drinking, and traveling) per day. This applies strictly to full-time University Students that have the responsibilities associated with that life such as studying, attending class, group projects, etc. and does not include extra activities such as cooking.

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

a. 12:10 pm

b. 40 mph

Step-by-step explanation:

Assuming you meant to type 1 ¹/₄ hours later.

a. First convert that to a improper fraction and then a decimal:

= 5/4

= 1.25 hours

1.25 hours in minutes is:

= 1.25 * 60

= 75 minutes

= 1 hour 15 minutes

The motorist left at 10:55.

= 1055 + 1 hour

= 11:55

Add 15 minutes:

= 12:10 pm

b. Speed = Distance / Time

= 50 / 1.25 hours

= 40 miles per hour

Answer:

8 + x bigger then 5

Good luck!!

Answer:Can you find the sum [5.5 + (-2.3)] + (-5.5 + 2.3) without performing any additions? - Slader.

1 answer

Missing: 7.25-5.5 ‎7.25)

Step-by-step explanation:

Answer:

H. 4.7

Step-by-step explanation:

Area=22

Side²=22

Side=√22

=4.69

=4.7

If you don't wanna do the calculations, just see the square of 3,4 and 5.

3²=9

4²=16

5²=25

22 is somewhere between 4² and 5².

4.7 is the answer.

Hope it helps :)

Answer: 42

Step by step:

42 is divisible by both 7 and 2

Answer:

44

Step-by-step explanation:

4 x 11 = 44

2 x 22 = 44

Answer/Step-by-step explanation:

Convert:

8m to _800_cm

K     H     D     B     D     C     M

                     8 -> 80 -> 800      

---------------------------------------------------------------------------------------------------

Interpret and simplify:

1 added to the difference of 12 and 9

1 + (12 - 9)

1 + (3) = 4

---------------------------------------------------------------------------------------------------

Write a positive or negative integer that represents the following:

A football team loses 14 yards on a play.

loses indicated a negative

-14

------------------------------------------------------------------------------------------------------

Evaluate:

  4          3

------- + -------

 20        12

  4 (3)     3 (5)

------- + -------

 20 (3)   12 (5)

 12          15         27

------- + -------  =  -------

 60        60         60

 27 ÷ 3           9

-------     =     --------

 60 ÷ 3          20

----------------------------------------------------------------------------------------------------------

Write the Prime Factorization of 24.

             24

            /    \

          2  ×  12

                  /  \

                2 × 6

                     /  \

                   2 × 3

Prime factorization = 2 × 2 × 2 × 3 or 2³ × 3

----------------------------------------------------------------------------------------------------------

Tell whether the ordered pair is a solution of the equation:

y = x + 7; (1, 6)

               (x, y)

6 = 1 + 7

6 = 8

Not a solution

----------------------------------------------------------------------------------------------------------

Simplify and Graph the following:

x = -2 - 3

x = -5

      ↑

<-----|--------------------------------->

      -5

      ↓

Don't worry about the other numbers. Put a dot on -5 and draw a line vertically (up and down).

----------------------------------------------------------------------------------------------------------

If the weight of a package is multiplied by (5/7). The result is 40.5 pounds. find the weight of the package.

x(5/7) = 40.5

---------  --------

÷(5/7)   ÷(5/7)

x = 56.7

----------------------------------------------------------------------------------------------------------

A = (1/2)bh

A= (1/2)(8)(5)

A = (1/2)(40)

A = (20)

A = 20in²

----------------------------------------------------------------------------------------------------------

I hope this helps!

Answer:

The slope a line perpendicular to the line whose equation is 4x+5y=35, is \(\frac{5}{4}\).

Step-by-step explanation:

1. Solve the given equation for y.

\(4x+5y=35\\\\5y=35-4x\\\\\frac{5y}{5} =\frac{35}{5} -\frac{4x}{5} \\\\y =7 -\frac{4x}{5}\\\\y = -\frac{4}{5}x+7\)

2. Identify the slope.

The slope of a linear equation is always the number x is being multiplied for. Hence, the value of this equation is \(-\frac{4}{5}\) .

3. Find the slope of the perpendicular line.

The slope of a perpendicular line is always the multiplicative and addition reciprocal of the initial function. This means that you will have to invert and fracction, and add the inverse sign before it. Let's do it by parts:

a) Find the multiplicative reciprocal (invert the fraction).

\(-\frac{5}{4}\)

b) Put the opposite sign before the fraction.

\(+\frac{5}{4}\)

4. Express a result.

The slope a line perpendicular to the line whose equation is 4x+5y=35, is \(\frac{5}{4}\).

Answer:

Step-by-step explanation:

Since,

Any number if divided by hundred then that no. is known as a percentage.

Here,

80 is divided by 100 i. e.

80 / 100

= 80% (Ans)

Answer:

Step-by-step explanation:

Write the problem as a mathematical expression.

Convert to decimal.

Multiply 0.8 by 100 to convert to a percentage.

Answer:

C = 2π(4.5 meters) = 9π meters

= 28.3 meters

The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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