Harry invests £5000 for 3 years.
He gets simple interest of 4% per year.
Work out the total interest Harry gets.

Assume a businessman has 7 suits and 8 ties. He is planning to take 4 suits and 3 ties with him on his next business trip. Possibilities of selection he have 1960.

A businessman has 7 suits

A businessman has 8 ties.

He is planning to take 4 suits and 3 ties with him on his next business trip.

We have to determining possibilities of selection he have.

Number of possible selections = \(^{7}C_{4}\times ^{8}C_{3}\)

Simplify

Number of possible selections = \(\frac{7!}{4!(7-4)!}\times\frac{8!}{3!(8-3)!}\)

Number of possible selections = \(\frac{7!}{4!3!}\times\frac{8!}{3!5!}\)

Number of possible selections = \(\frac{7\times6\times5\times4!}{4!\times3\times2\times1}\times\frac{8\times7\times6\times5!}{3\times2\times1\times5!}\)

After simplification we get

Number of possible selections = 7 × 5 × 8 × 7

Number of possible selections = 1,960

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Answer:

0,100,0.5,20

Step-by-step explanation:

My answer got removed cause I didn't put an explanation... you just plug in the numbers to the equation.

Answer:

OC

Step-by-step explanation:

I got it right on my test!

Answer: 12 and -4

Step-by-step explanation:

Assume the larger number is x and the smaller one is y.

In that case the relevant simultaneous equations are:

x + y = 8

2x + 4y = 8

Use substitution to find relative value of y:

x + y = 8

y = 8 - x

Use to solve equation:

2x + 4y = 8

2x + 4(8 - x) = 8

2x + 32 - 4x = 8

2x  - 4x= 8 - 32

-2x = -24

x = -24 / -2

x = 12

y = 8 - x

= 8 - 12

= -4

Answer:

1

Step-by-step explanation:

7x-7=3x-3

7x-3x=-3+7

4x=4

divide both sides by 4

hence,x=1

Answer:

The answer is B. 600

Step-by-step explanation:

Hope that helps!

Answer:

B. $600.00

Step-by-step explanation:

every 10hrs worked you are getting $120.00 so just add $120.00 every 10 hrs

Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Let point A be \((2, -6)\) and point B \((-1, -8)\)

\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-8 - (-6)}{-1 - 2} = \frac{-8 + 6}{-1 -2} = \frac{-2}{-3} = \frac{2}{3}\)

Use the point-slope formula and whichever point you want as , in this case I'll use

\(y - y_1 = m(x - x_1)\\y - (-6) = \frac{2}{3}(x - 2)\\y + 6 = \frac{2}{3}x - \frac{4}{3}\\y = \frac{2}{3}x - \frac{4}{3} - 6\\y = \frac{2}{3}x - \frac{14}{3}\)

The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.

Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles and circles. Trigonometry is used to calculate the measurements of angles, lengths, and areas of different geometric figures. It is also used to solve problems involving forces, motion, and velocity.

Sin2x = (2*15/17)*(-12/17) = -30/289
Cos2x = (2*15/17)*(-5/17) = -30/289
Tan2x = (2*15/17)/(-12/17) = -5/12
Since sinx = 15/17 and x terminates in quadrant 2, then x = -3π/17. The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.
Sin2x = 2*sinx*cosx = 2*(15/17)*(-12/17) = -30/289
Cos2x = 2*cosx*cosx - 1 = 2*(-12/17)*(-12/17) - 1 = -5/289
Tan2x = (2*sinx*cosx)/(cosx*cosx - sinx*sinx) = (2*(15/17)*(-12/17))/((-12/17)*(-12/17) - (15/17)*(15/17)) = -5/12

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Answer:

10N as the SI u it for net force is N

Step-by-step explanation:

The answer is:

F=MA

=2Kg×5m/s

=10N

Answer:

y>-2x-1 answer is b

-4x+y> 1 is c I believe

Step-by-step explanation:

Answer:

1.) Vertical angles. 2.) 76 degrees. 3.) 36 degrees.

Answer:

A.) True

Step-by-step explanation:

A set of outputs and inputs becomes a function when there is only one output per input. In this case, each "x" value only has one "y" value, making it a function.

The hypotheses to test the student's claim would be:

H₀: p = 0.19

Hₐ: p < 0.19

The appropriate hypotheses to test the student's claim would be:

H₀: p = 0.19 (The proportion of moving violations involving black cars is equal to 0.19)

Hₐ: p < 0.19 (The proportion of moving violations involving black cars is less than 0.19)

In this case, the null hypothesis (H₀) assumes that the proportion of moving violations for black cars is the same as the overall proportion of black cars in the population, which is 0.19. The alternative hypothesis (Hₐ) suggests that the proportion of moving violations for black cars is less than 0.19, supporting the student's claim that black cars are less likely to receive tickets for moving violations.

By conducting a statistical test, the student can assess the evidence and determine whether there is sufficient data to reject the null hypothesis and support the alternative hypothesis. The statistical test typically used in this scenario is a one-sample proportion test, such as the z-test or chi-square test, to compare the observed proportion (10 out of 70) with the expected proportion (0.19).

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The volume of the region is approximately 333.3.

The volume of the region bounded by the two equations z = x2 y2 and z = 20 − x2 − 2y2 can be calculated by setting up a triple integral and integrating it with respect to x, y, and z. To do this, we must first find the limits of integration.

For the x variable, the two equations both contain x2 so the limits of integration would be -√20 and √20. For the y variable, the equations contain y2 so the limits of integration would be -√10 and √10.

Finally, for the z variable, the limits of integration would be 0 and 20. Using these limits we can now write our triple integral, ∫∫∫(20 - x2 - 2y2)dx dy dz, and integrate it to find the volume of the region.

After integrating, we find that the volume is approximately 333.3.

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The slope of the line that connects (10,4) and (5,13) is -9/5.

Here given,

The two points are (10,4) and (5,13).

We have to find the slope that passes through the given points,

The formula to find slope(m) is,

The slope of the line that passes through (x1 , y1) and (x2,y2) is,

Slope(m) = y2 - y1 / x2 - x1

By substituting the values in x and y

Slope = 13 - 4 / 5 - 10

          = 9 / -5

Slope = -9/5

          = -1.8

Therefore the slope of line that passes through (10,4) and (5,13) is -9/5.

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The total number of positive integers with exactly four decimal digits that are divisible by 5 and by 7 is 255

There are a total of 12 positive integers with exactly four decimal digits that are divisible by 5 and by 7.
To find these numbers, we can start by finding the smallest and largest four-digit numbers that are divisible by 5 and 7. The smallest four-digit number that is divisible by 5 and 7 is 1050 (5 * 7 * 30) and the largest is 9945 (5 * 7 * 283).
Next, we can find how many multiples of 35 (5 * 7) are between 1050 and 9945. To do this, we can subtract the smallest multiple (1050) from the largest (9945) and divide by 35:
(9945 - 1050) / 35 = 8895 / 35 = 254
This means there are 254 multiples of 35 between 1050 and 9945. However, we need to add 1 to this number to include the smallest multiple (1050), so the total number of positive integers with exactly four decimal digits that are divisible by 5 and by 7 is 254 + 1 = 255.

Therefore, the answer is 255.

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Answer:

32.7

Step-by-step explanation:

Using the Pythagorean theorem, we can set an equation to 5^2+c^2=14^2,

which is equal to 196-25 = c^2, which is equal to c^2=171, therefore, c=\(\sqrt{171}\)

5*\(\sqrt{171}\)/2=32.69, rounded will equal to 32.7

Step by Step Solution:  to equal 4.25000

More Icon

STEP

1

:

17

Simplify ——

1

Equation at the end of step

1

:

17

—— ÷ 4

1

STEP

2

:

17

Simplify ——

1

Equation at the end of step

2

:

17

——

4

STEP

3

:

17

Simplify ——

4

Final result :

17

—— = 4.25000

4

Answer:

1h 22m

Step-by-step explanation:

Because 1/4 of an hour is 15m and 15X5=75 or 1h and 15m

then 1/3 of a lap would just be 33% of 15m which is 6.6m or round that up to 7 so 1h and 15m + 7m= 1h and 22m

hope that helped.

Answer:

2

Step-by-step explanation:

In a general estimation, a 1,000 sq ft house may have approximately 150-200 linear feet of baseboard. The exact number can vary based on factors such as the layout of the house, the number of rooms, and the height of the baseboard. It is advisable to measure the actual linear footage for accurate results.

Baseboards are typically installed along the bottom of walls to provide a decorative finish and cover the joint between the wall and the floor. They also protect the wall from damage caused by furniture or foot traffic. The linear footage required for baseboards is calculated by measuring the length of each wall in a room and summing them up. The height of the baseboard, usually ranging from 3 to 6 inches, can influence the total linear footage needed.

Factors such as corners, doorways, and irregular room shapes can increase the overall length of baseboard required. Additionally, if the house has different types of flooring, such as tile, carpet, or hardwood, transitions between these materials might necessitate additional baseboard. To get an accurate measurement, it is recommended to consult a professional installer or measure the walls yourself to determine the exact linear footage needed for the baseboard in a specific house.

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Answer:

5/9

Step-by-step explanation:

brainliest when possible.

a) The null hypothesis (H0) states that the population average amount dispensed is equal to 8 ounces. The alternative hypothesis (Ha) states that the population average amount dispensed is different from 8 ounces.

b) To test the hypothesis, we can perform a one-sample t-test. The sample mean is 7.983 ounces, which is slightly below the hypothesized value of 8 ounces. We want to determine if this difference is statistically significant.

c) By conducting the one-sample t-test, we can calculate the p-value associated with the observed sample mean of 7.983 ounces. The p-value represents the probability of obtaining a sample mean as extreme as the observed value, assuming that the null hypothesis is true.

If the calculated p-value is less than the significance level (0.05 in this case), we reject the null hypothesis in favor of the alternative hypothesis, indicating evidence that the population average amount dispensed is different from 8 ounces. If the p-value is greater than the significance level, we fail to reject the null hypothesis, suggesting that there is not enough evidence to conclude that the population average is different from 8 ounces.

The interpretation of the p-value in this case is that it represents the probability of observing a sample mean of 7.983 ounces or a more extreme value, assuming that the true population mean is 8 ounces. A small p-value indicates that the observed sample mean is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, a small p-value provides evidence against the null hypothesis and suggests that the population average amount dispensed is likely different from 8 ounces.

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Answer:

504.

Step-by-step explanation:

multiplication is just repeated addition. so it would be 84+84+84+84+84+84. multiply all 6 80's first to get 480. then multiply all 6 4's to get 24. 480+24=504

The inequality x+36>x4+1. The inequality's solution is the value of x.

x+36>4+1

x+36>5

x>5-36

x>-31

-31 value of x is a solution to the inequality.

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Answer: This is a binomial distribution problem with parameters n = 17 and p = 0.3, where n is the sample size and p is the probability of a defective bulb. We need to find the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective.

Let X be the number of defective bulbs in the sample. Then X has a binomial distribution with parameters n = 17 and p = 0.3, i.e., X ~ B(17, 0.3).

We want to find P(3 ≤ X ≤ 6). Using the binomial probability formula, we have:

P(3 ≤ X ≤ 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= (17 choose 3)(0.3^3)(0.7^14) + (17 choose 4)(0.3^4)(0.7^13) + (17 choose 5)(0.3^5)(0.7^12) + (17 choose 6)(0.3^6)(0.7^11)

≈ 0.1566 (rounded to four decimal places)

Therefore, the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective is approximately 0.1566.

Step-by-step explanation:

b (?) and c

m and n have the same slope (-2/5) so m//n

Answer:

4

Step-by-step explanation:

the second column and the second row so, the answer is 4

Answer:

x = 0     y = 2

Step-by-step explanation:

4x + 2 = -2x + 2

6x + 2 = 2

6x = 0

x = 0

y = 4(0) + 2

y = 2