Kellie called six friends with each call lasting 8 1/2 minutes. how long was Kellie on the phone

The answer is c because t must be less than 2.5 and more than 1.5.

Find this by separating the inequality into:

-90 < -32t - 10

&

-32t - 10 < -58

Simplify and you get 2.5 and 1.5

Graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

We have:

The velocity of the ball will be between –90 and –58 ft/s.

Let v be the velocity of the ball:

v lies between -90 and -58

-90 < v < -58

The above expression represents the inequality:

Or

-90 < -32t - 10

t < 2.5

And

-32t - 10 < -58

t > 1.5

The number line will be:

Open the circle on the number 1.5 and open circle at 2.5 and a line was drawn between this point.

Thus, graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.

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Answer:

b. 6.93 m.

Step-by-step explanation:

We have been given triangle ABC and we are asked to find the measure of a.

We will use law of sines to solve our given problem.

[tex]\frac{a}{\text{Sin}(A)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are opposite sides of angle A, B and C respectively.

First of all, we will find the measure of angle B using angle sum property.

[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]30^{\circ}+\angle B+90^{\circ}=180^{\circ}[/tex]

[tex]\angle B+120^{\circ}=180^{\circ}[/tex]

[tex]\angle B=180^{\circ}-120^{\circ}[/tex]

[tex]\angle B=60^{\circ}[/tex]

Upon substituting our given values in law of sines we will get,

[tex]\frac{a}{\text{Sin}(30^{\circ})}=\frac{12}{\text{Sin}(60^{\circ})}[/tex]

[tex]\frac{a}{0.5}=\frac{12}{\frac{\sqrt{3}}{2}}[/tex]

[tex]\frac{a}{0.5}=\frac{2*12}{\sqrt{3}}[/tex]

[tex]\frac{a}{0.5}*0.5=\frac{24}{\sqrt{3}}*0.5[/tex]

[tex]a=\frac{12}{\sqrt{3}}[/tex]

[tex]a=6.9282032302755\approx 6.93[/tex]

Therefore, the value of a is 6.93 meters and option 'b' is the correct choice.

Answer:

The slope of the line that passes through (-95, 31) and (-94, 6) is -25.

Step-by-step explanation:

The equation of a line has the following format:

[tex]y = ax + b[/tex]

In which a is the slope.

Passes through the point (-95, 31).

When [tex]x = -95, y = 31[/tex]

[tex]y = ax + b[/tex]

[tex]31 = -95a + b[/tex]

Passes through the point (-94, 6).

When [tex]x = -94, y = 6[/tex]

[tex]y = ax + b[/tex]

[tex]6 = -94a + b[/tex]

We have to solve the following system:

[tex]31 = -95a + b[/tex]

[tex]6 = -94a + b[/tex]

We want to find a.

From the first equation

[tex]b = 31 + 95a[/tex]

Replacing in the second equation:

[tex]6 = -94a + 31 + 95a[/tex]

[tex]a = -25[/tex]

The slope of the line that passes through (-95, 31) and (-94, 6) is -25.

Answer:

a1= 30 and r=0.9

Step-by-step explanation:

edge

The answer is 0.5.

To find the answer, understand the place value system in numbers.

The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number.

To find the answer, we need to understand the place value system. In the number 653,841, the digit in the hundreds place is 8, and the digit in the thousands place is 5. Therefore, 1/10 of the digit in the thousands place is 0.5.

So, the answer is 0.5.

A polynomial that is written as a product has been "factored completely."

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

In the expression Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.

Since we know that factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

A polynomial which can be written as a product has been "factored completely."

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Final answer:

To maximize revenue from football game ticket sales and concessions, we create a revenue function based on ticket price adjustments and evaluate changes in quantity demanded. The optimal price and attendance are found by analyzing the combined revenue function, deriving it with respect to the number of price decreases, and finding the maximum value of this function.

Explanation:

To determine the ticket price that should be charged by the university to maximize revenue from football game attendance, we need to analyze the effect of price changes on the quantity demanded. We can create a revenue function based on the given figures and the assumptions that a decrease of $3 in ticket price increases attendance by 10,000 people, and each person spends an average of $4.50 on concessions.

Let x represent the number of $3 decreases in price from the original $18. The ticket price can then be expressed as P = 18 - 3x, and attendance as A = 40000 + 10000x. The revenue from ticket sales is R1 = P × A, which gives us R1 = (18 - 3x) × (40000 + 10000x). The concession revenue per person is $4.50, so total concession revenue is R2 = 4.50 × A, which gives us R2 = 4.50 × (40000 + 10000x).

To maximize total revenue R = R1 + R2, we need to find the maximum of the function R = (18 - 3x) × (40000 + 10000x) + 4.50 × (40000 + 10000x). To find this, we can use calculus to take the derivative of R with respect to x and find the value of x that makes this derivative zero. This will be the critical point which we can then test to confirm it provides a maximum.

Answer:

6^1/20

Step-by-step explanation:

you multiply the two exponents

Answer:

[tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].

Step-by-step explanation:

As you can observe in the image attached, angles AMC and DMC are congruent, because if point C is the incenter of AMD, that means each line the forms such point is a bisector.

Remember that a bisector is a line that equally divides an angle.

So,

[tex]\angle AMC = \angle DMC\\3x+6=8x-49[/tex]

Solving for [tex]x[/tex], we have

[tex]6+49=8x-3x\\5x=55\\x=11[/tex]

Then, we substitute this value in each expression to find the angles.

[tex]\angle AMC = 3x+6 = 3(11)+6=33+6=39[/tex]

[tex]\angle DMC = 8(11)-49=88-49=39[/tex]

Therefore, the measures of those angles are [tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].

Answer:

x=-5, 5

Step-by-step explanation:

To find the solutions, use inverse operations to rearrange the equation to be equal to 0.

[tex]x^2-9-16=16-16\\x^2-25=0[/tex]

Factor the equation and then set each equal to 0 to solve for x.

[tex]x^2-25=0\\(x+5)(x-5)=0[/tex]

x+5=0

x=-5

x-5=0

x=5

C /4  = π

Took the test myself, this is the answer.

A fourth as much as the product of two thirds and 0.8 is ²/₁₅

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem !

First, we will translate this word problem into a mathematical equation.

The product of two thirds and 0.8

[tex]\frac{2}{3} \times 0.8[/tex]

A fourth as much as the product of two thirds and 0.8

[tex]\frac{1}{4} (\frac{2}{3} \times 0.8)[/tex]

[tex]= \frac{1}{4} (\frac{2}{3} \times \frac{4}{5})[/tex]

[tex]= \frac{1}{4} (\frac{2 \times 4}{3 \times 5})[/tex]

[tex]= \frac{1}{4} (\frac{8}{15})[/tex]

[tex]= \frac{1}{4} \times \frac{8}{15}[/tex]

[tex]= \frac{1 \times 8}{4 \times 15}[/tex]

[tex]= \frac{8}{60}[/tex]

[tex]= \frac{8 \div 4}{60 \div 4}[/tex]

[tex]= \boxed {\frac{2}{15}}[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent

Answer:

[tex]\frac{4\sqrt{6x}}{2x}[/tex]

Explanation:

The problem we are given is

[tex]4\sqrt{\frac{3}{2x}}[/tex]

We can write the square root of a fraction as a fraction with a separate radical for the numerator and denominator; this gives us

[tex]4\times \frac{\sqrt{3}}{\sqrt{2x}}[/tex]

We can write the whole number 4 as the fraction 4/1; this gives us

[tex]\frac{4}{1}\times \frac{\sqrt{3}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}}{\sqrt{2x}}[/tex]

We now need to "rationalize the denominator."  This means we need to cancel the square root in the denominator.  In order to do this, we multiply both numerator and denominator by √(2x); this is because squaring a square root will cancel it:

[tex]\frac{4\sqrt{3}}{\sqrt{2x}}\times \frac{\sqrt{2x}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}\times \sqrt{2x}}{2x}[/tex]

When multiplying radicals, we can extend the radical over both factors:

[tex]\frac{4\sqrt{3} \times \sqrt{2x}}{2x}\\\\=\frac{4\sqrt{3\times 2x}}{2x}\\\\=\frac{4\sqrt{6x}}{2x}[/tex]

Answer:

The correct answer is ^4sqrt24x^3/2x or B on edge.

Step-by-step explanation:

The best way to group these ages into six intervals is from 40-44 to 65-69.

A frequency distribution table gives an idea about the data point or interval and its frequency.

The age of the Presidents given as

57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46

The smallest number ( age) is 42 and the largest number (age ) is 69

To make 6 intervals in this gap of 27 , each interval should be of length 5

Therefore the intervals will be

40-44

45-49

50-54

55-59

60-64

65-69

This is the best way to group into intervals.

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Final answer:

The best way to group the ages of U.S. Presidents into six intervals for a frequency table is by intervals of five years each, starting at age 42 and ending at age 71, to cover the entire range and maintain equal width for all intervals.

Explanation:

When grouping ages into intervals for a frequency table, it's best to have intervals that are of equal width and cover the entire range of data without overlap. For the ages of U.S. Presidents starting their terms, which range from 42 to 69, we could divide this range into six intervals in a way that makes sense for this data set.

First, find the range by subtracting the youngest age from the oldest: 69 - 42 = 27. Next, divide this range by the number of desired intervals (6), which gives us 4.5. We can round this to 5 to make the intervals more practical. Thus, each age interval will span 5 years. Starting at 42, the six intervals would be: 42-46, 47-51, 52-56, 57-61, 62-66, and 67-71.

This grouping covers all the ages and each interval is of equal width, making it easy to interpret the frequency table.

We have that for the Question, it can be said that  the area under the standard normal curve between z 1.5 and z 2.5 is

P(1.5 &2.5) =0.06

From the question we are told

How to find the area under the standard normal curve between z 1.5 and z 2.5?

Generally the equation for the probability is mathematically given as

P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)

Where

P(Z < 2.5) = 0.99

P(Z < 1.5) = 0.93

From Z Table

Therefore

P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)

P(1.5 &2.5) =0.06

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