Write a numerical expression for the verbal expression. eighteen divided by the sum of two and seven

Answer:

83 %

Step-by-step explanation:

If 5 out of 30 got an A, that means that

30 -5 = 25

25 out of 30 did not get and A

25/30 = .8333333 = 83.33333 %

Rounding to the nearest whole percent

83 %

The pharmacist should mix 9 g of a power to make a larger amount of the medicine

To solve this problem, we have to state the equation using the information of the problem

Information about the problem:

Calculating the rate of the medicine with the 1st mixed:

rate = mass(1)/ volume(1)

rate = 5g / 45cm3

rate = 0.11 g/cm3

Calculating how much power the pharmacist needs for the volume(2):

mass(2) = rate * volume(2)

mass(2) = 0.11 g/cm3 * 81 cm3

mass(2) = 9 g

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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average inflation rate of cold drink will be 100%

Inflation is the term used to describe an increase in the price of goods and services that households buy. It is determined by how quickly these prices fluctuate. Prices frequently rise with time, but they can also fall (a situation called deflation).

You will subtract the starting price (A) from the later price (B), and divide it by the starting date (A). Then multiply the result by 100 to get the inflation rate percentage.

FORMULA FOR FINDING AVERAGE INFLATION = ((B-A)/A)*100

            plugging in the values =

∵ given in the question that cost will double in the next 8 years i.e.

                                                                             = Rs. 4.50 * 2

                                                                             = Rs.9.00

∴ when we plug in  the values in the formula we get

                                                 = ((9-4.5)/4.5) * 100

                                                 = 100 % inflation rate

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The baseball was faster than the club head will be incorrect.

Conversion means to convert the same thing into different units.

A baseball pitch traveled 128 feet per second. During a golfer's drive, the club head speed was 99 miles per hour.

We know that in one mile, there are 5280 feet. And in one hour, there are 3600 seconds.

Then the speed of the golfer's drive will be

⇒ 99 x 5280 feet / 3600 seconds

⇒ 145.2 feet per second

The speed of the club head is faster than the baseball.

The baseball was faster than the club head will be incorrect.

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The probability of selecting two socks of same color is 0.96.

According to the given question.

Total number of green socks = 4

Total number of yellow socks = 6

So, the total number of socks in a drawer = 4 + 6 = 10

Since as we know that, the probability of an event is computed as: P(E) = Number of favourable outcome /Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.

So, the probability of selecting a green scoks = 4/10 = 2/5

And the probability of selecting a yellow socks = 6/10 = 3/5

Therefore, the probability of selecting two socks of same color

= probability of selecting both the green socks or probability of selecting both the yellow socks

= [( 2/5) + (2/5)] × [(3/5)+(3/5)]

= (4/5) × (6/5)

= 24/25

= 0.96

Hence, the probability of selecting two socks of same color is 0.96.

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Answer:

$750

Step-by-step explanation:

I = interest

p = principle

r = rate

t = time

I = prt  Plug in what you know and solve for p

360 = p (.06)(8)

360 =p.48  Divide both sides by .48

750 = p

The principal is deposited in the account is $750.

Given that, rate of interest =6%, time period = 8 years and simple interest = $360.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

Now, 360 = (P×6×8)/100

⇒ 360 = 48P/100

⇒ 48P = 36000

⇒ P = 36000/48

⇒ P = $750

Therefore, the principal is deposited in the account is $750.

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The combination of hours that Keitaro can walk and run in a month to reach his goal will be A. 2 hours walking; 12 hours running

From the information, Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles.

The equation is

3w + 6r ≥ 36

3w + 6r ≤ 90

The combination of hours that Keitaro can walk and run in a month to reach his goal will be 2 hours walking; and 12 hours running.

This will be:

3w + 6r ≤ 90

3(2) + 6(12)

6 + 72 = 78

Therefore, 78 is less than 90.

The correct option is A.

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Answer: B

Step-by-step explanation: the square root of 2 cannot really be expressed as a fraction where both the numerator and the denominator are integers.

Answer:

B

Step-by-step explanation:

P(ac) means that it's 100%

The circumference of the given circle is: 16πcm.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Given: Area of a circle = 64π cm²

To find: Circumference of the circle.

Finding:

We know that the formula of the area of a circle = πr²,

On comparing it with the given value, we get:

πr² = π(64)

πr² = π(8)²

8² = r²

r = 8cm (as the side of a circle can never be negative).

Also, the formula of the circumference of a circle = 2πr

Thus, for the circle having radius 8 cm, circumference = 2π(8) = 16πcm.

Hence, The circumference of the given circle is: 16πcm.

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The option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.

What is a quadratic equation ?

A quadratic equation is an equation which contains a single variable of degree 2 and its general form is ax² + bx + c = 0.

The height of firework is represented by a quadratic equation which is 16t² + 128t.

Let's find out that at what time the rocket will be at height of 64 feet.

So,

16t² + 128t = 64 feet

or

16t² + 128t - 64 = 0

or

t² + 8t - 4 = 0

We know that quadratic equation is in form ax² + bx + c = 0.

Using the quadratic formula to find value of t :

[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]

t = [ -8 ± √(8² - (4 × 1 × - 4))] / ( 2 × 1 )

t = [ - 8 ± 8.94 ] / 2

t = -4 ± 4.47

So , the value of t can be either -4 + 4.47 or -4 - 4.47 which is equal to 0.47 or - 8.47 seconds. Time can't be negative , so t = 0.47 or 0.5 seconds.

Therefore , the option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.

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The length of u by using sine rule is 7.4 to the nearest 10th of an inch.

In mathematics, sine rule is a trigonometric method which relates the angle and side of a triangle. We can say that by using the sine rule we can find the side of any triangle if we knows the angle and vice versa. This rule is also known as law of sines.

Formulas for sine rule:

If we have three sides a, b, c and angle say A, B and C respectively .Then sine rule is :

[tex]\frac{Sin A}{a} = \frac{Sin B}{ b} = \frac{Sin C}{c}[/tex]

In the given question,

Sine rule will be used to get the unknown side of the triangle.

According to the rule;

[tex]\frac{Sin U}{u} = \frac{Sin V}{ v} = \frac{Sin W}{w}[/tex]

Given w = 3 in, ∠W=23° and ∠U=73°,  substitute into the equation above to get u we have;

we can write the eq. as

[tex]\frac{Sin U}{u} = \frac{Sin W}{w}[/tex]

[tex]= > u = \frac{w \ sinu}{sinw} \\\\= > u = \frac{3 sin73}{sin 23} \\\\= > u = \frac{2.87}{0.39}\\ \\= > u = 7.398 = 7.4[/tex]

Hence,  length of u is 7.4 inches to the  nearest 10th of an inch.

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Answer:

x= 32

Step-by-step explanation:

3x-2+3x-10= 180 (sum of angles in straight line)

6x-12=180

6x=192

6x/6= 192/ 6

x = 32

Step-by-step explanation:

3x - 2 ° + 3x - 10° = 180°

reason : being angle in linear pair ...

6x - 12 = 180°

6x = 180° + 12

6x = 192°

[tex] x = \frac{192}{6} \\ [/tex]

x = 32°

Now ,

3x - 2 °

= 3 × 32 - 2

= 96 - 2

= 94°

Again ,

= 3x - 10°

= 3 × 32 - 10°

= 86°

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Answer:

30.55 + 6.18 = $36.73

Step-by-step explanation:

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Odd Multiples of 7767 are 1, 3, 9, 863, 2589, 7767.The greatest common divisor of [tex]$6a^2 49a 108$[/tex] = 6×1×49×1×108= 31,752 and

2a9=2×1×9=18

The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor (GCD) in mathematics. The greatest common divisor of two numbers x and y is shown for x and y. As an illustration, the GCD of 8 and 12 equals 4, or. The words "divisor" and "factor" can be swapped out in the name "largest common divisor" so that alternative names such as "highest common factor" (HCF), etc. can be used instead. In the past, the term biggest common measure has been used to refer to the same idea.

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Step-by-step explanation:

THE POINT WHERE

[tex]f( - 4) = ( { - 4})^{2} + 1 \\ f( - 4) = 16 + 1 \\ f( - 4) = 17[/tex]

Now we have point (-4,17)

the gradient of the tangent line at that point of f(x) is the first derivative f'(x)=2x at that point

f'(x) =m

f'(-4)=2(-4)

f'(-4)=-8

The gradient therefore is -8

the general equation of a straight line is given by

[tex]y = mx + c \\ 17 = ( - 8)( - 4) + c \\ 17 = 32 + c \\ c = 17 - 32 \\ c = - 15 \\ \\ y = - 8x - 15[/tex]

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how much is in the spice mix? context is necessary

The measure of angle A in the triangle is 18°

The angles in the triangle are given as:

m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°

The sum of angles in a triangle is 180

So, we have

m∠A + m∠B + m∠C = 180

Substitute the known values in the above equation

So, we have:

2x − 24 + x + 8 + 4x + 49 = 180

Evaluate the like terms

7x = 147

Divide both sides by 7

x = 21

Substitute x = 21 in m∠A = (2x − 24)°

m∠A = (2 * 21 − 24)°

Evaluate

m∠A = 18°

Hence, the measure of angle A in the triangle is 18°

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By compatibility principle of inequalities we complete the following sentence:

If p and q are negative integers such that p² > q², then p³ < q³. (Correct choice: B)

According to the statement, the elements p and q are negative integers such that p² > q². By the sign law, the product of two negative numbers is always equal to a positive number, then by compatibility principle:

p² > q²                   Given

p · p > q · q            Definition of power

p < q                       Compatibility principle

p³ < q³                    Compatibility principle / Result

Please notice that the inequality symbol, that is, from "<" to ">" and viceversa, changes when the compatibility principle is applied in the given inequality.

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Answer:   To find the average rate of change, divide the change in y-values by the change in x-values

Step-by-step explanation:

In words, the ratio of the number of jeans bought to the cost is four to thirty two.

We are told that you just bought 4 pairs of jeans for $32.

Now, since you bought 4 pairs for a cost of $32, then we can say that the ratio to represent the number jeans per dollars is;

4 :32

Thus, writing this in words we can say that the ratio of the number of jeans bought to the cost is four to thirty two.

Alternatively, we can also express it as a fraction with numerator and denominator as 4/32.

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Complete question is;

You just bought 4 pairs of jeans for $32. write a ratio and sentence comparing the number of jeans bought to the cost

Answer:

80 seconds

Step-by-step explanation:

rate x time = gallons

[tex]\frac{.7}{2}[/tex]t = 28  Multiply both sides by  [tex]\frac{2}{.7}[/tex]

t =  80

The value of [m + √n] is 183.

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See attachment for the graph of the function and the features

The function is given as

h(x) =(x - 1)^2 - 9

The x-intercept

Set h(x) to 0

So, we have

(x - 1)^2 - 9 = 0

Add 9 to both sides

(x - 1)^2 = 9

Take the square root of both sides

x - 1 = ±3

This gives

x = 1 ± 3

Expand

x = (1 - 3, 1 + 3)

Evaluate

x = (-2, 4)

Hence, the x-intercepts are x =2 and x = 4

The y-intercept

Set x to 0

So, we have

h(0) = (0 - 1)^2 - 9

Evaluate

h(0) = -8

Hence, the y-intercept is h(x) =-8

The vertex

We have

h(x) =(x - 1)^2 - 9

Expand

h(x) = x^2 - 2x + 1 - 9

Differentiate

h'(x) = 2x - 2

Set to 0 and solve for x

2x - 2 = 0

This gives

x = 1 --- this represents the axis of symmetry

Substitute x = 1 in h(x) =(x - 1)^2 - 9

h(1) =(1 - 1)^2 - 9

Evaluate

h(1) = -9

Hence, the vertex of the function is (1, -9)

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The rule(s) of algebra illustrated by the statement is the identity property of algebra

The statement is given as:

1 · (1 + x) = 1 + x

The identity property of algebra states that:

1 * a = a or a * 1 = a

In the above (given) statement, we can see that the expression 1 + x is multiplied by 1 to given 1 + x

This can be illustrated as

1 * a = a

The rule(s) of algebra that illustrates the above equation is the identity property of algebra

Hence, the rule(s) of algebra illustrated by the statement is the identity property of algebra

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[tex]16 : (200 \cdot 100) =[/tex]

[tex]16 : 20000 = 0.0008[/tex]

Answer:

8

Step-by-step explanation:

To solve this problem we use PEMDAS; Parenthesis, Exponents, Multiply, divide, add, subtract

Let's set up an equation:

16/200*100

Now let's solve:

16/200=0.08

Now we multiply 0.08 by 100

0.08*100=8

Thus, our answer is 8

Answer:

I don't know

Step-by-step explanation:

I don't know

The surface area of a cube with side length of 6 1/2 inches is 253.5 square in

The formula for calculating the surface area of cube is expressed as:

Surface area = 6L^2

where

L is the side length of the cube

Substitute

SA = 6(13/2)^2

SA = 6 * 169/4

SA = 3 * 169/2

SA = 253.5 square in

Hence the surface area of a cube with side length of 6 1/2 inches is 253.5 square in

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89 degrees

Triangles will always have 180 degrees. This means that given 2 angles, we can find the missing measurement.

Setting Up an Equation

To help us solve for the unknown angle, a, we can set up an algebraic equation. To make this equation remember that all 3 internal angles sum to 180.

This is only one equation that you could set up to represent this situation.

Solving For a

Now that we have an equation we can begin to solve it. First, combine like terms that are on the same side of the equation.

Next, subtract 91 from both sides.

To check our answer we can plug it back into the original equation.

This means that the missing angle must be 89 degrees.