John has 10 quarters 11 nickels, 14 dimes and 159 pennies
his bank? He added that money to the $46.76 he had in his
savings account. How much money does John have in his
account now?

Answer:

13.2/hour

Step-by-step explanation:

10% of 12 = 1.2

12+1.2=13.2

The number line that shows the solutions of x < 5

A number line is a visual representation of the real numbers, ordered from left to right, with zero in the middle. It is typically a straight line that extends infinitely in both directions, with evenly spaced markings that represent specific points along the line.

The solution of x < 5 should consist of number less than 5

The inequality used is less than and hence should have values saying less than

Other options has numbers more than 5 such as 6 except option B

Learn more about number line at:

https://brainly.com/question/25230781

#SPJ1

Answer:

A change from 45 to 60 represents a positive change (increase) of 33.3333333333%

Step-by-step explanation:

Percent change = 60 - 45

45

× 100 = 33.333333333333 % (increase)

Answer:

33.3% increase

Step-by-step explanation:

Percent of Change =

\( \frac{change}{original} \)

The change would be 15:

60 - 45 = 15

So the percent of change would be:

15/45 = 1/3 = 33.3% increase

Hope this helps! Brainliest would be appreciated!

Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.

We can use the following formula to calculate ROI:

ROI = (gain from investment - cost of investment) / cost of investment

where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.

Using the values given in the question, we can calculate the ROI as:

ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000

ROI = 0.16 or 16%

Therefore, the return on the investment is 16%.

Know more about rate of investment,

https://brainly.com/question/25790997

#SPJ1

Using the Divergence Theorem, we get the flux of F across the closed surface S is π/2 (27√2 - 27).

To apply the Divergence Theorem, we will first compute the divergence of F as follows -

div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 1 + 1 + 1

= 3

Now we will calculate the flux of F across the closed surface S that completely surrounds T. By the Divergence Theorem, this is equal to the triple integral of the divergence of F over the region T and is given by -

∫∫S F•n dS = ∭T div(F) dV

We can describe the region T using cylindrical coordinates:

0 ≤ r ≤ 2

-π/2 ≤ θ ≤ π/2

0 ≤ z ≤ √(9 - r sin θ)

The bounds on r and θ come from the fact that the half cylinder is contained within the plane x = 2, and the plane y = ±3. The bounds on z come from the equation of the half cylinder.

Now we can write the triple integral as follows -

∭T div(F) dV = ∫0^2 ∫-π/2^π/2 ∫0^√(9 - r sin θ) 3 r dz dθ dr

Evaluating this integral, we get,

∭T div(F) dV = π/2 (27√2 - 27)

Therefore, the flux of F across the closed surface S is π/2 (27√2 - 27).

Read more about the divergence theorem:

brainly.com/question/19699905

#SPJ4

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

for such more question on Bryan invested

https://brainly.com/question/20690803

#SPJ8

An expression for given sequence of operations is: j + 3^9

In this question, we need to write an expression for the sequence of operations described below.

raise 3 to the 9th power, then add the result to j

Consider the part of given statement,

raise 3 to the 9th power

We write this as: 3^9

then we add this result to j.

So, we get an expression: 3^9 + j

Therefore, an expression for given sequence of operations is: j + 3^9

Learn more about expression here:

https://brainly.com/question/1859113

#SPJ9

The scale which is equivalent to 1 cm to 1 km is 1 to 100,000. Hence 3rd option is correct

Cm: The SI prefix centi stands for a factor of 1/100, making a centimetre a length unit that is equal to one-tenth of a metre. In the now-outdated centimetre-gram-second system of units, the centimetre served as the fundamental unit of length.

Km: A kilometre is a measurement unit for both length and distance. It is a metric unit of measurement. Additionally, miles, which are equivalent to one kilometre, can be used to describe the distance. Although miles and kilometres are equivalent in size, they have different values.

Learn more about conversions:

https://brainly.com/question/16290674

#SPJ9

Answer:

Your answer is.....

170 students

Mark it as brainlist answer . follow me for more answer.

Step-by-step explanation:

A circle, when using degrees, have 360 degrees. 1/360 of a circle can be calculated by multiplying the two numbers.

\(\frac{1}{360}*360=1\)

Therefore, the answer for the question is

1/360 of a circle measure 1 degree

Answer:

Dylan is 10 years old, and Genesis is 11.

Step-by-step explanation:

If Genesis and Dylan's age are consecutive integers, and Genesis is older, we can represent their ages as:

Dylan's age: x

Genesis' age: x+1

This would mean Genesis is a year older than Dylan.

The product of their ages is 110.

We can write an equation:

x×(x+1)=110

x²+x=110 (Distribute x)

x²+x-110=0 (Move 110 to the other side)

You can solve this by the quadratic equation, by factoring or by completing the square

I'll solve it by the quadratic equation:

We must first find the coefficients a, b and c, and then plug it into the formula.

\(x = \frac{ - 1 + - \sqrt{ {1}^{2} - 4 \times 1 \times - 110} }{2 \times 1} \\ x = \frac{ - 1 + - \sqrt{1 + 440} }{2} \\ x = \frac{ - 1 + - 21}{2} \)

Since we have a ± symbol, we get 2 real solutions, x1 and x2.

x=-1±21/2

x1=-1+21/2

x1=20/2

x1=10

x2=-1-21/2

x2=-22/2

x2=-11

Since their age can't be negative, x2 can't be a solution, so Dylan's age must be 10, and Genesis' age must be 11.

Hope this helps, and let me know if you need help with another method to solve this problem!

Answer:

4

Step-by-step explanation:

Answer: 4.8

Step-by-step explanation:

Answer:

4x+x=40

5x+40

x=8

8, 32

Step-by-step explanation:

Answer:

8 and 32 are the numbers

Step-by-step explanation:

4x + x = 40

4x + x= 5x

5x + 40

40/5= 8

x= 8

and

40-8= 32

x= 32

Answer:

t= 0.4933

t ≥ t ( 0.025 ,8 ) = 2.306

Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.

Step-by-step explanation:

We state our null and alternative hypotheses as

H0: ud= 0 Ha: ud≠0

The significance level is set at ∝= 0.05

The test statistic under H0 is

t= d`/ sd/√n

which has t distribution with n-1 degrees of freedom

The critical region is t ≥ t ( 0.025 ,8 ) = 2.306

Computations

Student       Scores before      Scores after    Difference           d²

                        reading book                    ( after minus before)

1                          720                   740             20                       400

2                        860                   860              0                           0

3                        850                   840             -10                       100

4                        880                   920             40                       1600

5                        860                   890             30                        900

6                        710                    720              10                         100

7                       850                    840              -10                       100

8                      1200                  1240             40                        1600

9                      950                    970              20                           40

∑                    6930                  8020           140                         4840

d`= ∑d/n= 140/9= 15.566

sd²= 1/8( 4840- 140²/9) = 1/8 (4840 - 2177.778) = 2662.22/8= 332.775

sd= 18.2422

t= 3/ 18.2422/ √9

t= 0.4933

Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.

According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

Learn more about period in: https://brainly.com/question/23532583
#SPJ1

Answer:

False

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

West University:

15 out of 100, so:

\(p_W = \frac{15}{100} = 0.15\)

\(s_W = \sqrt{\frac{0.15*0.85}{100}} = 0.0357\)

East University:

12 out of 100, so:

\(p_E = \frac{12}{100} = 0.12\)

\(s_E = \sqrt{\frac{0.12*0.88}{100}} = 0.0325\)

Test the difference in driving abilities at the two universities:

At the null hypothesis we test if there is no difference, that is, the subtraction of the proportions is 0, so:

\(H_0: p_W - p_E = 0\)

At the alternative hypothesis, we test if there is a difference, that is, if the subtraction of the proportions is different of 0. So

\(H_1: p_W - p_E \neq 0\)

The test statistic is:

\(z = \frac{X - \mu}{s}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that \(\mu = 0\)

From the two samples:

\(X = p_W - p_E = 0.15 - 0.12 = 0.03\)

\(s = \sqrt{s_W^2+s_E^2} = \sqrt{0.0357^2+0.0325^2} = 0.0483\)

Value of the test statistic:

\(z = \frac{X - \mu}{s}\)

\(z = \frac{0.03 - 0}{0.0483}\)

\(z = 0.62\)

P-value of the test and decision:

The p-value of the test is the probability that the proportions differ by at least 0.03, which is P(|z| > 0.62), that is, 2 multiplied by the p-value of z = -0.62.

Looking at the z-table, z = -0.62 has a p-value of 0.2676.

2*0.2676 = 0.5352.

The p-value of the test is 0.5352 > 0.05, which means that the difference in driving is not statistically significant at the .05 significance level, and thus the answer is False.

The measure of each inscribed angle at T and S is 72.5 degrees, and the sum of their measures is: 145 degrees

What is inscribed angle ?

An inscribed angle is an angle formed by two chords of a circle that have a common endpoint on the circle. The vertex of the inscribed angle is on the circle, and the sides of the angle intersect the circle at two distinct points.

There are some important properties of inscribed angles:

According to the question:
If the inscribed angles of T and S intercept the same arc, then they must be equal in measure. Let's call the measure of each angle x.

Since the sum of the measures of the angles in a triangle is 180 degrees, we can set up an equation to find the measure of the third angle in triangle TSY:

x + x + measure of angle YTS = 180 degrees

Simplifying the equation, we get:

2x + measure of angle YTS = 180 degrees

But we know that the measure of angle YTS is equal to half the measure of arc YZ, since it is an inscribed angle intercepting the same arc. So:

measure of angle YTS = 1/2 * measure of arc YZ = 1/2 * 70 degrees = 35 degrees

Substituting this value into our equation, we get:

2x + 35 degrees = 180 degrees

Solving for x, we get:

2x = 145 degrees

x = 72.5 degrees

Therefore, the measure of each inscribed angle at T and S is 72.5 degrees, and the sum of their measures is:

72.5 degrees + 72.5 degrees = 145 degrees

To know more about inscribed angle visit:
https://brainly.com/question/15899344
#SPJ1

They will be when they pass each other at 44 4/9 mins.

This is a classic question on Speed, time, & distance.

1. When time traveled in each segment is constant, then average speed is simple mean of speeds.

2. When distance traveled in each segment is constant, then average speed is reciprocal of simple mean of reciprocal of speeds. It is basically called Harmonic mean.

So this question falls in the category of 2.

=> So, average speed = Reciprocal of mean of reciprocals of 40 & 50.

=> Average speed = Reciprocal of mean of 1/40 & 1/50.

=> Average speed = Reciprocal of (1/40 + 1/50)/2

= Reciprocal of (5+4)/400

= 44 4/9 mins

Hence, they will be when they pass each other at 44 4/9 mins.

To know more about speed check the below link:

https://brainly.com/question/4931057

#SPJ1

Answer:

2 1/5

Step-by-step explanation:

First you make both fractions into 5 becomes 25/5. 2 4/5 becomes 14/5. Then you would just subtract 25/5 - 14/5 = 11/5 then make it a mixed number 2 1/5.

Answer:

It would be 2.2 as a decimal, or 11/5 (2 1/5)

Step-by-step explanation:

It's quite simple.

Start by turning 2 4/5 into an improper fraction, then turn 5 into a fraction. By doing that you should get 25/5 - 14/5. Subtract to get 11/5.

hope this helped!

The quotient ^3√60 / ^3√20 simplifies to 2.

To simplify the quotient ^3√60 / ^3√20, we can apply the rules of exponents for radicals.

Let's start by simplifying the individual cube roots:

^3√60 = ^3√(2^2 × 3 × 5) = 2^2 × ^3√(3 × 5) = 2^2 × ^3√(15).

Similarly,

^3√20 = ^3√(2^2 × 5) = 2 × ^3√5.

Now we can rewrite the original quotient using these simplified forms:

^3√60 / ^3√20 = (2^2 × ^3√15) / (2 × ^3√5).

Since we have the same cube root in the numerator and denominator, we can cancel them out:

^3√60 / ^3√20 = (2^2 × ^3√15) / (2 × ^3√5) = 2^2 / 2 = 4 / 2 = 2.

For more such questions on quotient

https://brainly.com/question/30339946

#SPJ8

Answer:

9

Step-by-step explanation:

27 is the compliment of 63

108 is the suppliment of 72

72 - 63 is the difference aka 9

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

for such more questions on vector

https://brainly.com/question/15519257

#SPJ8

Answer:

2.90

Step-by-step explanation:

im not completly shous though

Answer:

170 cm³

Step-by-step explanation:

V = πr²h

= 3.14 * (3)² * 6

= 3.14 * 9 * 6

= 169.56 cm³

= 170 cm³

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

Answer:

He should sell his CD's for $2.

Step-by-step explanation:

Each crate contains 60 blank CD’s and each crate cost $35.

This means that he will pay $35 for 60 CD's.

How much should he sell his CD’s to make a profit of $85?

He will sell each of the 60 CD's for x, which means that his earnings will be of 60x.

Profit: Earnings - Cost = 60x - 35

To make a profit of $85

\(60x - 35 = 85\)

\(60x = 120\)

\(x = \frac{120}{60}\)

\(x = 2\)

He should sell his CD's for $2.

Answer:

Step-by-step explanation:

After buying the ticket, the amount with him = 50 - 7 = 43

p ≤ 50 - 7

p ≤ 43

Answer:

p≤ 43

Step-by-step explanation:

50-7=43

so now Mr.smith will have $43 to spend

p is less than or equal to 43