Martha made a purchase for $70.20 including 8% sales tax.
What was the total before tax?

Answer: He travelled 392 km that day.

Step-by-step explanation:

We are given that,

Speed of electric car = 56 km per hour.

Time = 7 hours

We know that,

Distance = Speed x Time

If he travelled 7 hours on that day, then Distance traveled in 7 hours on that day= (56 km per hour)  x (7 hours)

i.e. Distance traveled in 7 hours on that day== 392 km

Hence, he travelled 392 km that day.

Answer:

A. 2

Step-by-step explanation:

∛8 = 2

There is only one correct value to it so it can't be negative and positive 2, the answer is positive 2 so,

= 2

Answer:

Step-by-step explanation:

8/3

Answer:

27

Step-by-step explanation:

Given that the total number of people protesting is 81. These people are either male - Student or non student or Females (student or non students)

Given that there are 36 males then number of females

= 81 - 36

= 45

If there are 18 females non students then the number of females protesting that are students

= 45 - 18

= 27

Answer:

5. 1/4, 4/16

6. 4/5, 16/20

7. 1/3, 6/18

8. 2/9, 4/18

9. 1/3, 3/9

Step-by-step explanation:

Hope that helps!

Answer:

Do it your self

Step-by-step explanation:

Gross

Answer:

30.5

Step-by-step explanation:

Answer:

-5.5

Step-by-step explanation:

[tex]2x+7=-4\\2x=-4-7\\2x=-11\\x=-5.5[/tex]

Answer:

-11/2

Step-by-step explanation:

Let the number be a

(2a)+7= -4

2a= -4-7

2a= -11

a= -11/2

Answer:

The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta= b^{2} - 4ac[/tex]

Quadratic equation:

[tex]ax^2 + bx + c = 0[/tex]

The rock reaches a maximum height of 676 feet above the ground after 1.5 seconds.

This means that:

[tex]-\frac{b}{2a} = 1.5[/tex]

[tex]y_{v} = -\frac{b^2-4ac}{4a} = 676[/tex]

If the rock hits the ground below the ledge 8 seconds after it is thrown

This means that:

[tex]64a + 8b + c = 0[/tex]

Relation of b and a:

[tex]-\frac{b}{2a} = 1.5[/tex]

This means that:

[tex]b = -3a[/tex]

Relationship of c and a:

[tex]64a + 8b + c = 0[/tex]

[tex]64a - 24a + c = 0[/tex]

[tex]c = -40a[/tex]

Finding a:

[tex]y_{v} = -\frac{(-3a)^2-4a(-40a)}{4a} = 676[/tex]

[tex]9a^2+160a = -2704a[/tex]

[tex]9a^2 + 2864a = 0[/tex]

[tex]a(9a + 2864) = 0[/tex]

Since it is a quadratic equation, a cannot be 0.

[tex]9a + 2864 = 0[/tex]

[tex]9a = -2864[/tex]

[tex]a = -\frac{2864}{9}[/tex]

[tex]a = -318.22[/tex]

Finding b and c:

[tex]b = -3a = -3(-318.22) = 954.67[/tex]

[tex]c = -40a = -40(-318.22) = 12728.89[/tex]

The quadratic equation is given by:

[tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]

The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]

Answer:

3 and 6.

Step-by-step explanation:

Write and evaluate the expression. Then, check all that apply.

Felix divided his shirts into three equal groups. Evaluate when s = 18.

The expression is

The expression is

The expression is s/3

The expression is

The answer is

The answer is 6.

Answer:

1/12

Step-by-step explanation:

Multiply across

Hope this helps

Answer:

1/6 chance of rolling a 4

Answer:

A. c = kn

Step-by-step explanation:

The cost c varies directly as the numbers n of pencils

This means that c is a multiplication of a constant by n, which is the number of pencils. So the equation for the cost is given by:

[tex]c = kn[/tex]

In which k is the constant of proportionality, that is, the cost of each pencil. So the correct answer is given by option A.

Answer:

x = 15

Step-by-step explanation:

Assuming 3x and x-60 are in degrees, you can use:

cos(a) = sin(a+90)

To rewrite the equation as:

sin(3x) = sin(x-60+90)

sin(3x) = sin(x+30)

3x = x+30

2x = 30

x = 15

But, solving 3x = x+30 which simplifies to x=15 is not the only solution to this equation, as you can see in below picture. Finding all solutions is a bit more work, but maybe that is not required in your case.

Answer:

sax

SI = $432

P = $1200

rate = x

time = x

= 432 = t×p×r / 100

= 432 = x × 1200 × x / 100

= 432 = x × 12 × x

= 432 = 2x × 12

= 432/12 = 2x

= 6 = 2x

= 6 ÷ 2 = x

= 3 = x

The rate of interst is 3%

Step-by-step explanation:

Answer:

1. It is not appropriate to use the normal curve, since np = 7.4 < 10.

2. The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.

Step-by-step explanation:

Binomial approximation to the normal:

The binomial approximation to the normal can be used if:

np >= 10 and n(1-p) >= 10

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

The proportion of U.S. adults with high blood pressure is 0.2. A sample of 37 U.S. adults is chosen.

This means, respectively, that [tex]p = 0.2, n = 37[/tex]

Is it appropriate to use the normal approximation to find the probability that more than 48% of the people in the sample have high blood pressure?

np = 37*0.2 = 7.4 < 10

So not appropriate.

It is not appropriate to use the normal curve, since np = 7.4 < 10.

Part 2:

Now n = 82, 82*0.2 = 16.4 > 10, so ok

Mean and standard deviation:

By the Central Limit Theorem,

Mean [tex]\mu = p = 0.2[/tex]

Standard deviation [tex]s = \sqrt{\frac{0.2*0.8}{82}} = 0.0442[/tex]

Find the probability that more than 32% of the people in this sample have high blood pressure.

This probability is 1 subtracted by the pvalue of Z when X = 0.32. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.32 - 0.2}{0.0442][/tex]

[tex]Z = 2.72[/tex]

[tex]Z = 2.72[/tex] has a pvalue of 0.9967.

1 - 0.9967 = 0.0033

The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.

Answer:

25.6

Step-by-step explanation:

16*2=32

32*0.8=25.6

Answer:

25.6

Step-by-step explanation:

16x.8=12.8

because he makes it every half mile we have to multiply by 2\

12.8*2=25.6

if he walks 16 miles he makes 25.6

Step-by-step explanation:

so basically they are asking you to subtract, hope this helps, use a calculator if needed

Answer:

She will pay $13.9 for 7.56 liters

Step-by-step explanation:7.56 minus 3.78 equals to 3.78. This means we can just simply add another $6.95, so $6.95 plus $6.95 equals to $13.9

Answer:

let marked price = x

on 10% discount, price= x-10%of x

=x-(10x/100)

=x-(x/10)

=9x/10

on further 10% discount, total discount = 10% of 9x/10

=10/100 * 9x/10

= 9x/100

= 9%of x

hence, the single discount given on marked price is 9%

Step-by-step explanation:

My calculator says 97.5

Answer:

195/2

Step-by-step explanation:

60/8=15/2

15/2*13=195/2

Answer:

A =224 in ^3

Step-by-step explanation:

Answer:

56in squared

Step-by-step explanation:

Answer:

1) D and R are NOT independent events

2) The probability of electing a Republican president and an economic decline in 2020 is 0.224

3) If we experience an economic decline in 2016, the probability that a Republican president will have been elected in 2020 is 0.9739

4) the probability of economic decline or a Republican president elected in 2020 or both is 0.646

Step-by-step explanation:

Let "D" represent the event of an economic decline, and "R" represent the event of election of a Republican president

Given that;

P(D) = 0.23

P(R) = 0.64

Conditional P(D | R) =  0.35

1) Are R and D independent events?

we know that two events A & B are independent events if; P(B | A) = P(B)

here, P(D | R) =  0.35 and P(D) = 0.23

so; P(D | R) ≠ P(D)

Therefore D and R are NOT independent events

2) The probability of electing a Republican president and an economic decline in 2020;

we know that;

P(D | R) = P(D ∩ R) / P(R)

we substitute

0.35 = P(D ∩ R) / 0.64

P(D ∩ R) = 0.35 × 0.64

P(D ∩ R)  = 0.224

Therefore, The probability of electing a Republican president and an economic decline in 2020 is 0.224

3) If we experience an economic decline in 2016, what is the probability that a Republican president will have been elected in 2020?

P(R | D) = P(D ∩ R) / P(D)

we substitute

P(R | D) = 0.224 / 0.23

P(R | D) = 0.9739

Therefore, If we experience an economic decline in 2016, the probability that a Republican president will have been elected in 2020 is 0.9739

4) the probability of economic decline or a Republican president elected in 2020 or both

P(D ∪ R) = P(D) + P(R) - P(D ∩ R)

we subtitute

P(D ∪ R) = 0.23 + 0.64 - 0.224

P(D ∪ R)  = 0.646

Therefore, the probability of economic decline or a Republican president elected in 2020 or both is 0.646

Answer:

A

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The car is moving in a circular track with a radius of 1.9 miles. The distance covered by the car if the track is revolved once = 2π * radius of the track.

a) Since the car has swept out an angle of 212 degrees, the distance covered by the race car = [tex]\frac{212}{360}*2\pi(1.9)=7.03 \ miles[/tex]

b) If the car traveled 4.9 miles, the angle swept out (θ) is:

[tex]4.9= \frac{\theta}{360} * 2\pi r\\\\\theta=\frac{4.9}{2\pi (1.9)}*360 \\\\\theta=147.76^o=147.76^o*\frac{\pi}{180} \\\\\theta=2.58\ rad[/tex]

c) h = distance covered, t = time in hourss.

Hence:

h = 85.5t

The race-car's motion round the track is a repeating motion that can be

described by a sinusoidal function.

The correct responses are;

Reasons:

Known parameters are;

Radius of the track, r = 1.9 miles

Point the car starts = 3 O'clock

Speed of the car = 85.5 mph

Required:

Distance swept out when the car traveled an angle of 212°.

Solution;

Distance of one complete turn = 2·π·r

Angle of one complete turn = 360°

Therefore, at 212°, we have;

[tex]\dfrac{212^{\circ}}{360^{\circ}} \times 2 \times 1.9 \times \pi \approx 7.03[/tex]

Required:

The measure of the angle swept out by the car if the car has travelled 4.9 miles.

Solution;

Let, θ represent the angle, we have;

[tex]\dfrac{\theta}{2 \cdot \pi} \times 2 \times 1.9 \times \pi \approx 4.9 \ miles[/tex]

We get;

[tex]{\theta} = \dfrac{4.9 \ miles}{2 \times 1.9 \ miles \times \pi } \times 2\cdot \pi \approx 2.58 \ radians[/tex]

Required:

The function, h, that gives the distance of the above the horizontal

diameter of the track (in miles) in terms of the number of hours since the

race-car started driving, t.

Solution;

The function that gives the car height can be presented as follows;

The angular velocity, ω = [tex]\dfrac{v}{r}[/tex]

Therefore;

[tex]\omega = \dfrac{85.5 \ mph}{1.9 \ miles} = 45 \ rad/hour[/tex]

The general form of the sinusoidal function is h = A·sin[k·(θ - b)] + c

Therefore, we get;

h = 1.9·sin[k·(θ - b)] + c

The period, T = 2·π/ω = 2·π/k

Therefore, given that ω·t = θ, we get;

h = 1.9·sin[ω·t - b] + c = 1.9·sin[45·t - b] + c

The vertical sift, c, and the horizontal shift, b, can both be taken as zero,

given that the sin(0) = 0, therefore;

h = 1.9·sin[0] + c = c = 0, such that the at the start, t = 0, the car is at a

distance of h = 0 above the horizontal line.

The function, h, that gives the distance of the car above the

horizontal track, in terms of the number of hours since the car started

driving, t, is therefore;

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