Find the gradients of the lines a and b

Answer:

=√2/4

Step-by-step explanation:

\(sin(3\pi /4) = \frac{\sqrt{2}}{2} \\\\and \\\\cos(5\pi /3) = \frac{1}{2} \\\\\)

Therefore, sin(3π/4) × cos(5π/3) = √2/2 × 1/2 = √2/4

Answer:

x=7

Step-by-step explanation:

BRAINLIEST?

Answer:

x = 7

Step-by-step explanation:

Answer:

b=-1

Step-by-step explanation:

Let's solve your equation step-by-step.

0.5(5−7b)=8−(4b+6)

Step 1: Simplify both sides of the equation.

0.5(5−7b)=8−(4b+6)

0.5(5−7b)=8+−1(4b+6)(Distribute the Negative Sign)

0.5(5−7b)=8+−1(4b)+(−1)(6)

0.5(5−7b)=8+−4b+−6

(0.5)(5)+(0.5)(−7b)=8+−4b+−6(Distribute)

2.5+−3.5b=8+−4b+−6

−3.5b+2.5=(−4b)+(8+−6)(Combine Like Terms)

−3.5b+2.5=−4b+2

−3.5b+2.5=−4b+2

Step 2: Add 4b to both sides.

−3.5b+2.5+4b=−4b+2+4b

0.5b+2.5=2

Step 3: Subtract 2.5 from both sides.

0.5b+2.5−2.5=2−2.5

0.5b=−0.5

Step 4: Divide both sides by 0.5.

0.5b/0.5=−0.5/0.5

b=−1

By showing that the corresponding sides are not proportional we know that the Triangles △fgh and △jih are not similar.

To prove that triangles △fgh and △jih are not similar, we need to show that at least one pair of corresponding sides is not proportional.
Let's compare the side lengths:

Side fg does not have a corresponding side in △jih.
Side gh in △fgh corresponds to side hi in △jih.
Side fh in △fgh corresponds to side ij in △jih.

By comparing the side lengths, we can see that side gh/hj and side fh/ij are not proportional.

Therefore, triangles △fgh and △jih are not similar.

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Triangle FGH (△FGH) is not similar to triangle JIH (△JIH) because their corresponding angles are not congruent and their corresponding sides are not proportional.

To prove that triangle FGH (△FGH) is not similar to triangle JIH (△JIH), we need to show that their corresponding angles and corresponding sides are not proportional.

1. Corresponding angles: In similar triangles, corresponding angles are congruent. If we compare the angles of △FGH and △JIH, we find that angle F in △FGH corresponds to angle J in △JIH, angle G corresponds to angle I, and angle H corresponds to angle H. Since the corresponding angles in both triangles are not congruent, we can conclude that the triangles are not similar.

2. Corresponding sides: In similar triangles, corresponding sides are proportional. Let's compare the sides of △FGH and △JIH. Side FG corresponds to side JI, side GH corresponds to side IH, and side FH corresponds to side HJ. If we measure the lengths of these sides, we can see that they are not proportional. Therefore, the triangles are not similar.

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Anil Kumar should pay a compound amount of Rs. 23,397.12 at the end of 2 years.

Compound interest is a method of calculating interest where the interest earned is added to the principal amount, and the resulting sum becomes the new principal for the next period's interest calculation. This process is repeated until the end of the investment period.

The formula to calculate the compound interest is:

\(A = P(1 + r/n)^(^n^t^)\)

Where,

A = Amount after the given time

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Time duration for which the interest is calculated (in years)

In this case, Anil Kumar took a loan of Rs. 20,000 from a bank at the rate of 8% per annum, compounded half-yearly, for 2 years. Therefore, we can plug in the values as follows:

P = Rs. 20,000

r = 8% per annum = 0.08 (as a decimal)

n = 2 (since the interest is compounded half-yearly)

t = 2 years

Now, we can calculate the compound amount using the above formula:

\(A = P(1 + r/n)^(^n^t^)\)

\(A = 20,000(1 + 0.08/2)^(^4^)\)

\(A = 20,000(1 + 0.04)^4\)

\(A = 20,000(1.04)^4\)

\(A = 23397.1712\)

Therefore, Anil Kumar should pay a compound amount of Rs. 23,397.123 at the end of 2 years.

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A: 95 people dislike both

B: 81

C: 21

Answer:

Thanks for the points!!

Step-by-step explanation: dawggggggg

Answer:

whats up , whats the question ?

Step-by-step explanation:

Answer:

the circumstance is 43.98

Malia that uses 51 yards of ribbon to make 17 bows will have to use 204 yards of ribbon to make 68 bows

To solve this problem we will use a rule of three with the problem information:

17 bows-------- 51 yards of ribbon

68 bows-------- x

Applying the rule of three we get:

x = (68 bows * 51 yards of ribbon) /17 bows

x = 204 yards of ribbon

It describes the proportionality of 3 known data and an unknown data. When you have more than 3 known facts that are involved in the proportionality, it is known as a compound rule. The rule of three is also known as a direct proportions.

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Answer:

\(\huge\boxed{\bf\:x = 10}\)

Step-by-step explanation:

\(20x + 19 = 219\)

Subtract 19 from both the sides of the equation.

\(20x = 219 - 19\\20x = 200\)

Now, divide both sides of the equation by 20.

\(x = \frac{200}{20} \\\boxed{\bf\:x = 10}\)

\(\rule{150}{2}\)

Answer:

10

Step-by-step explanation:

20x+19=219

20x=219-19=200

20x=200

x=200/20

=10

The length of the cuboid is 12.8 cm.

Let's solve the problem to find the length of the cuboid.

Volume of the cuboid:

The volume of a cuboid is calculated by multiplying its length, width, and height. In this case, we are given the width as 10 cm and the height as 4 cm.

Since we don't know the length, let's denote it as L.

Therefore, the volume of the cuboid can be expressed as:

Volume of cuboid = Length × Width × Height

Volume of cuboid = L × 10 cm × 4 cm

Volume of cuboid = 40L cm³

Volume of the cube:

The cube is three quarters (3/4) full with water.

This means that the volume of water in the cube is 3/4 of the volume of the cube.

The volume of a cube is given by the formula:

Volume of cube = Side length³

In this case, the side length of the cube is 8 cm.

Therefore, the volume of the cube is:

Volume of cube = 8 cm × 8 cm × 8 cm

Volume of cube = 512 cm³

Equating the volumes:

Since the water from the cuboid is poured into the cube, the volume of the water in the cuboid must be equal to the volume of the water in the cube. So we have:

40L cm³ = 512 cm³

Solving for the length of the cuboid:

To find the length L, we can rearrange the equation as follows:

40L cm³ = 512 cm³

L = 512 cm³ / 40 cm³

L = 12.8 cm

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Answer:

(x+5)/(2x+3)

Step-by-step explanation:

So we know the top part is difference of two squares. So thats (x+5)(x-5)

The bottom part

Firstly you do 2 times -15= -30

Now we need to find two numbers with a difference of 7 but multiply to give 30.

30

1 x 30

2 x 15

3 x 10

5 x 6

From here we can see 3-10=-7 and multiply to make -30

So we do 2x²-10x+3x-15

simplify this in two different parts: 2x²-10x and 3x-15

2x(x-5) and 3(x-5)

Therefore we get (2x+3)(x-5)

(x+5)(x-5)/(2x+3)(x-5)

x-5 is common so they cancel each other out leaving you with

(x+5)/(2x+3)

I hoped this helped :)

Answer:

Cost of a play station game = $11.3

Cost of each water ride = $22.6

Step-by-step explanation:

Entrance tickets = $89.97

Royal meal = $10.85

Cost of a play station game = x

Cost of each water ride = 2x

Find the cost of a water ride

Entrance tickets = Royal meal + 1 play station game + 3 water rides

89.97 = 10.85 + 1(x) + 3(2x)

89.97 = 10.85 + x + 6x

89.97 = 10.85 + 7x

89.97 - 10.85 = 7x

79.12 = 7x

x = 79.12/7

x = 11.302857142857

Approximately to the nearest tenth

x = $11.3

Cost of a play station game = x = $11.3

Cost of each water ride = 2x

= 2(11.3)

= $22.6

Rounding up to the nearest whole number, we need a sample size of 15682 measurements to obtain a margin of error of ±0.001 with 98% confidence

To determine the number of measurements needed to obtain a margin of error of ±0.001 with 98% confidence, we need to use the following formula:

n = [(z-value)² * σ²] / E²

Where:

n = sample size

z-value = the critical value for the desired confidence level, which is 2.33 for 98% confidence

σ = the standard deviation of the population, which is unknown

E = the maximum error or margin of error, which is 0.001

Since the standard deviation of the population is unknown, we can estimate it using the standard deviation of the sample. Assuming that the sample standard deviation is similar to the population standard deviation, we can use the sample standard deviation of 0.03 in this case.

Substituting the given values, we have:

n = [(2.33)² * (0.03)²] / (0.001)²

n = 15681.93

Rounding up to the nearest whole number, we need a sample size of 15682 measurements to obtain a margin of error of ±0.001 with 98% confidence.

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The back-to-back stem-and-leaf plot or parallel boxplots can be use to compare. GPAs for successful students are generally higher. A significant relationship exists between GPA and credit hours for successful students. An applicant with a 3.5 GPA is likely to be successful, as the predicted value is closer to successful students' values.

To compare the GPAs for the two groups, an appropriate graphical display could be a back-to-back stem-and-leaf plot or parallel boxplots. Based on the graph, we can observe that successful students generally have higher GPAs than unsuccessful students.

To determine if there is a significant relationship between GPA and mean number of credit hours per semester for successful students, we can use a t-test for the slope or linear regression t-test.

Given the provided computer output, with a t-value of -5.90 and a p-value of 0.000, we can reject the null hypothesis and conclude that there is a significant relationship between GPA and mean number of credit hours per semester for successful students.

Using the regression equation to predict the number of credit hours for an applicant with a GPA of 3.5,

For the successful group predicted hours = 23.514 – 2.7555(3.5) = 13.86975

For the unsuccessful group predicted hours = 24.200 – 3.485(3.5) = 12.0025

we get a predicted value of 13.86975 for successful students and 12.0025 for unsuccessful students.

Since the actual value of 14 is closer to the predicted value for successful students, we can infer that this applicant is likely to be successful in the Ph.D. program.

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--The given question is incomplete, the complete question is given

" The statistics department at a large university is trying to determine if it is possible to predict whether an applicant will successfully complete the Ph.D. program or will leave before completing the program. The department is considering whether GPA (grade point average) in undergraduate statistics and mathematics courses (a measure of performance) and mean number of credit hours per semester (a measure of workload) would be helpful measures. To gather data, a random sample of 20 entering students from the past 5 years is taken. The data are given in photo.

a. Use an appropriate graphical display to compare the GPAs for the two groups.(provide names only) Write a few sentences commenting on your display.

b. For the students who successfully completed the Ph.D. program, is there a significant relationship between GPA and mean number of credit hours per semester?

Give a statistical justification to support your response.

c. If a new applicant has a GPA of 3.5 and a mean number of credit hours per semester of 14.0, do you think this applicant will successfully complete the Ph.D. program? Give a statistical justification to support your response. "--

The correct statement is (C) A two-tailed test will be performed since the alternative hypothesis states that the parameter is not equal to the hypothesized value.

In hypothesis testing, we have a null hypothesis (H0) and an alternative hypothesis (H1 or Ha). The null hypothesis typically represents the status quo or no effect, while the alternative hypothesis represents the claim or effect we are trying to test.

In this case, the null hypothesis would state that getting a flu shot does not reduce the risk of developing the flu. The alternative hypothesis would state that getting a flu shot does have an effect on reducing the risk of developing the flu, whether it is an increase or decrease.

Since the alternative hypothesis states that the parameter (effect of flu shot) is "not equal to" the hypothesized value (no effect), we need to perform a two-tailed test. This means we will consider both the possibility of a significant decrease and a significant increase in the risk of developing the flu due to the flu shot.

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Many children develop the ability to do simple arithmetic problems during their early childhood years, typically between the ages of 4 and 6. Correct option is a).

During this time, children start to understand basic mathematical concepts such as counting, addition, and subtraction. They may also begin to recognize and name numbers and use basic math vocabulary. However, it's important to note that every child develops at their own pace and some may show these skills earlier or later than others. It's also important for parents and caregivers to provide opportunities for children to practice and reinforce these skills through activities such as counting objects, playing number games, and solving simple math problems.

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The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

1/8

The probability of getting a head or a tail when flipping a coin is 1/2.  

Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.

The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.

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The speed of the faster car is 40 miles/hr.

both cars travel for same time , so let that time be 't'

car 1 :

distance travelled = 75 miles

let the speed of the car be = x miles/hr

∴ time (t)  = distance / speed

              t  =   75 / x               .............(1)

car 2 :

distance travelled = 100 miles

speed of the car is = x + 10 miles/hr  ( already provided )

∴  time ( t) = distance / speed

            t  = 100/ (x+10)        ..............(2)

    now as the time for both the cases is same  , so we equate eqn (1) and eqn (2) .

∴ 75/x  =  100/ (x+10)

3x + 30 = 4x

x = 30

so the speed of the 1st car will be 30 miles / hr

and the speed of the 2nd car ( faster car ) will  be x + 10 = 40 miles/hr

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The solution for the compound inequality is 4 < b ≤ 5.

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

The question gives:

3b + 2 < 5b - 6 ≤ 2b + 9

You can write the previous compound inequality as:

3b + 2 < 5b - 6 (1)

5b - 6 ≤ 2b + 9 (2)

         3b + 2 < 5b - 6

         3b-5b < -6 -2

          -2b < -8

            2b >8

            b >4

         5b - 6 ≤ 2b + 9

         5b-2b  ≤ 9+6

          3b ≤ 15

          b ≤ 5

Combining the intervals, you have 4 < b ≤ 5.

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Therefore, the volume of the paper cone to the nearest tenth is 418.7 inches cubed.

The volume of the paper cone that Gretchen made to hold a gift for a friend is given by;V= (1/3)πr²hWhere;r = radius of the paper coneh = height of the paper coneπ = 3.14

Given that;Height of the paper cone (h) = 16 inches Radius of the paper cone (r) = 5 inchesWe are to find the volume (V) of the paper cone to the nearest tenth of an inch.

To obtain the volume of the paper cone, we can substitute the values of r and h in the formula above to obtain;

\(V= (1/3)\pir^2hV\)= \((\frac{1}{3} ) \times 3.14\times5^2 \times16V = (\frac{1}{3} ) \times 3.14\times25\times16V = (\frac{1}{3}) \times 1256V=418.7\)

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Step-by-step explanation:

Adding A Negative Number

Now let's see what adding and subtracting negative numbers looks like:

add subtract +- goes down

We can add weights (we are adding negative values)

the basket gets pulled downwards (negative)

Example: 6 + (−3) = 3

is really saying

"Positive 6 plus Negative 3 equals Positive 3"

We could write it as (+6) + (−3) = (+3)

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given,  Tamara sold x + 20, Rueben sold 3( x + 20 ) pizzas, and Dwayne sold x pizzas.

We can simplify and combine the expressions for the total number of pizzas sold by each person:

Total pizzas sold = Dwayne's pizzas + Tamara's pizzas + Rueben's pizzas

= x + (x + 20) + 3(x + 20) [substituting the given expressions]

= x + x + 20 + 3x + 60

= 5x + 80

Therefore, the total number of pizzas sold by all three people is 5x + 80.

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Complete question:

Dwayne sold x pizzas. tamara sold x + 20. rueben sold 3( x + 20 ) pizzas.

State the comparison among all of three about the sold Pizzas.

1. x + 4 = 0 or x + 7 = 0

x = -4 or x = -7

2. 3x - 7 = 0 or 2x + 5 = 0

x = 7/ 3 or x = -5/ 2

3. x + 5 = 0 or x -8 = 0

x = -5 or x = 8

4. (x - 6) = 0 or (3x + 7) = 0

x = 6 or x = -7/ 3

5. 5x + 2 = 0 or 2x + 1 = 0

x = -2/ 5 or x = -1/ 2

1. (x+4)(x+7)=0

We have that;

Zero product property;

x + 4 = 0 or x + 7 = 0

x = -4 or x = -7

2.  (3x-7)(2x+5)=0

We have that;

Zero product property ;

3x - 7 = 0 or 2x + 5 = 0

x = 7/ 3 or x = -5/ 2

3. x² -3x - 40=0

x² -8x + 5x - 40 = 0

factorize the common multipliers

x(x - 8) + 5(x - 8) = 0

Zero product property;

x + 5 = 0 or x -8 = 0

x = -5 or x = 8

4. 3x² - 11x - 42=0

3x² +7x - 18x - 42 = 0

Factorize further

x(3x + 7) - 6(3x + 7) = 0

Zero product property;

(x - 6) = 0 or (3x + 7) = 0

x = 6 or x = -7/ 3

5. 10x² + 9x + 2 = 0

10x² + 5x + 4x + 2 = 0

Factorize

5x( 2x + 1) + 2 (2x + 1) = 0

Zero product property;

5x + 2 = 0 or 2x + 1 = 0

x = -2/ 5 or x = -1/ 2

Thus, the zero product property states that the product of two non-zero elements is not zero

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By evaluating the given relation, we conclude that the correct options are A, D, and G.

We have the relation:

k = ∛(V/7)

Such that this relation gives us pairs of the form (V, k).

So, to check if the points belong to the graph of the relation, we need to evaluate the points on the given relation and see if the relation is true.

A) (0, 0) gives:

Evaluating in V = 0

k = ∛(0/7) = 0

So this point belongs.

B) (1, 1) gives:

k= ∛(1/7) = 0.52

So we have the point (1, 0.52) and the point  (1, 1)  then does not belong to the graph.

We just need to do that for all the points, evaluate V and see if k gives the same value as in the point.

With this method, we will see that the correct options are:

D) (7, 1)

k= ∛(7/7) = 1

G) (56, 2)

k= ∛(56/7)  =   ∛(8) = 2

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Answer:

Please see attachment.

Step-by-step explanation:

Since there are no answer choices, I will just show you the graphs for each one.

Remember the dashed lines means it is either greater than, or less than.

The solid lines are either greater than or equal to, or less than or equal to.

Hope this helps!

If not, I am sorry.

The solutions of the equation given as |2/3x + 2| − 8 = 0 are x = 9 and x = -15

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

to determine the solutions of the equation:

The equation is given as:

|2/3x + 2| − 8 = 0

Start by adding 8 to both sides of the equation.

So, we have

|2/3x + 2| = 8

Next, we remove the absolute value expression

So, we have;

2/3x + 2 = 8 and 2/3x + 2 = -8

Subtract 2 from both sides of the equation

2/3x = 6 and 2/3x = -10

Multiply the equation by 3/2

x = 9 and x = -15

Hence, the solutions of the equation given as |2/3x + 2| − 8 = 0 are x = 9 and x = -15

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Complete question:

Determine the solutions of the equation:

|2/3x+2−8=0

Ox= -9 and x = 9

Ox= -15 and x = 4

Ox= -15 and x = 9

Ox= -15 and x = 15

Answer:

2 hours and 30 minutes.

Step-by-step explanation:

First you must add $50 and $75. Then add two $75, to get $200. Then, Multiply $1.25 by 30.

Hope this helps :)

(If it did please make this brainliest.)