Please help I’ll give brainliest what is the slope of the line
-1/2
1/2
-2
2

The measure of the angle m∠ACB which is an interior angle of the triangle ∆ABC is equal to 73°.

The interior angles of a triangle have the sum total of 180° when added up. In other words, the interior angles of a triangle is equal to 180°.

angle A = 180 - 108 {sum of angles on a straight line EC}

angle A = 72

angle B = 180 - 145 sum of angles on a straight line}

angle B = 35

m∠ACB = 180 - (35 + 72) {sum of interior angles of a triangle}

m∠ACB = 180 - 107

m∠ACB = 73°

Therefore, the measure of the interior angle m∠ACD for the triangle ∆ABC is equal to 73°

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Answer:

a. y=x^2

Step-by-step explanation:

desmos graphing calculator

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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a. A one-sample hypothesis test should be conducted to analyze the impact of exercise breaks on the workers' sense of well-being.

b. Based on the given information and a significance level of 0.05, we have sufficient evidence to conclude that exercise breaks have a statistically significant impact on the workers' sense of well-being.

Formulate the null and alternative hypotheses:

The null hypothesis (H0) states that exercise breaks do not improve the workers' sense of well-being, while the alternative hypothesis (Ha) states that exercise breaks do improve their sense of well-being.

Select the significance level (α):

The significance level (α) is given as 0.05, which represents the maximum probability of rejecting the null hypothesis when it is true.

Perform the hypothesis test and calculate the P-value:

The P-value is found to be 0.042.

Compare the P-value to the significance level:

Since the P-value (0.042) is less than the significance level (0.05), we reject the null hypothesis.

Therefore, based on the given information and a significance level of 0.05, we have sufficient evidence to conclude that exercise breaks have a statistically significant impact on the workers' sense of well-being.

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Answer:

Step-by-step explanation:

\(18a ^{2} (c−8)÷27ab(c−8)\)

Answer:

3(2/9) ounces of sprinkles each sundae (3.222222.....)

Step-by-step explanation:

12 divided into 4  = 3 ounces

(8/9)/4  is the same as  (8/9) x(1/4) = 8/36 = 2/9

3 ounces and 2/9 ounces

Each sundae will have 3 2/9 ounces of sprinkles on it.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Chloe has 12 8/9 ounces of sprinkles and 4 sundaes, so she will put 12 8/9 / 4 = 3 2/9 ounces of sprinkles on each sundae.

To break this down, 12 8/9 can be simplified to 12 + 8/9 = 12 + 8/9 = 12 + 4/9 = 12 4/9.

When we divide 12 4/9 by 4, we get 3 2/9.

So each sundae will have 3 2/9 ounces of sprinkles on it.

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Answer:

2 cups

Step-by-step explanation:

18/6 = 3

3 x 2/3 = 6/3

6/3 = 2

Answer:

Step-by-step explanation:

13

A discount bond selling for $15,000 with a face value of $20,000 in one year has a yield to maturity of 33.33 percent. So the option d is correct.

A discount bond selling for $15,000 with a face value of $20,000 in one year.

Yield to maturity (YTM) can be calculated using a variety of methods, including bond pricing formulas, the dividend discount model, and the capital asset pricing model.

The most common way to calculate YTM is using a bond pricing formula, which uses the current market price of the bond, the par value, the coupon rate, and the number of years to maturity to determine the yield. Additionally, investors can use online tools and calculators to determine YTM.

yield to maturity = (20,000 - 15,000)/15,000 x 100%

yield to maturity = 5000/15000 x 100%

yield to maturity = 0.3333 x 100%

yield to maturity = 33.33%

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The complete question is:

A discount bond selling for $15,000 with a face value of $20,000 in one year has a yield to maturity of

a. 3 percent

b. 20 percent

c. 25 percent

d. 33.33 percent

The apparent capacity of a glass vessel refers to its perceived size or volume based on external dimensions, while the actual capacity represents the true volume of the vessel, taking into account both interior and exterior dimensions.

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♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

X=131°

Step-by-step explanation:

y= 101°

z= 52°

X= ?

BCD is a ∆

therefore y= Z + BCD angle (exterior angle of a ∆ is equal to the sum of opposite interior Angles)

angle BCD= y-z

= 101°-52°

=49°

also X= 180°- angle BCD (sum of angles on a straight line)

X= 180°-49°

X= 131°

Answer:

x = 131°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

y is an exterior angle of the triangle, then

∠ DCB + z = y , that is

∠ DCB + 52 = 101 ( subtract 52 from both sides )

∠ DCB = 49°

∠ DCB and x are adjacent angles and sum to 180°

∠ DCB + x = 180

49° + x = 180° ( subtract 49° from both sides )

x = 131°

domain is x

range is y

plot point example (x,y) or (domain,range)

if its a circle

(a,b) = center

r = radius

(x-a)²+ (y-b)²=r²

socratic

The lines of symmetry in this particular picture are the horizontal and vertical lines.

If you were to look at the first quarter, and the vertical line reflects the curves to the second quarter.

Then, if you were to look at the horizontal line, you would see that the line reflects the entire top half to the bottom.

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In conclusion the correct solution is 1.54 as the spending multiplier.

The spending multiplier is a measure of the impact of changes in spending on overall economic output. It represents the amount by which a change in spending is multiplied throughout the economy. In this case, the question provides a marginal propensity to consume (MPC) of 0.65.

The MPC represents the portion of additional income that individuals choose to spend rather than save. Since the MPC is 0.65, it means that for every additional dollar earned, individuals will spend 65 cents and save the remaining 35 cents.

To calculate the spending multiplier, we take the reciprocal of the MPC. In this case, the reciprocal of 0.65 is approximately 1.54. This means that a change in spending of $1 will result in a total change in economic output of approximately $1.54.

For example, if there is an increase in government spending by $100 million, the total impact on the economy will be approximately $154 million. This is because the initial increase in spending will lead to additional income for individuals, who in turn will spend a portion of that income, leading to further rounds of spending and economic activity.

Therefore, the correct answer is 1.54 as the spending multiplier.

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The population of E. coli bacteria after 104 minutes would be approximately 4.42 x 10¹⁰.

The population of E. coli bacteria doubles every 30 minutes, which means that the growth rate is proportional to the current population. Let P(t) be the population at time t in minutes. Then, we have:

dP/dt = kP,

where k is the proportionality constant. We can solve this differential equation using separation of variables:

dP/P = k dt

ln(P) = kt + C

where C is the constant of integration. To determine C, we can use the initial condition that the population is 1000 when t = 0:

ln(1000) = C

C = ln(1000)

Therefore, the expression for the population growth is:

P(t) = 1000 \(e^(^k^t^)\)

To find the value of k, we use the fact that the population doubles every 30 minutes:

P(30) = 1000 \(e^(^k^*^3^0^)\) = 2000

\(e^(^k^*^3^0^)\)= 2

k = ln(2)/30

Substituting this value of k into the expression for P(t), we get:

P(t) = 1000 \(e^(^(^l^n^(^2^)^/^3^0^)^*^t^)\)

To find the population after 104 minutes, we substitute t = 104 into the expression:

P(104) = 1000 \(e^(^(^l^n^(^2^)^/^3^0^)^*^1^0^4^)\) ≈ 4.42 x 10¹⁰

Therefore, the population of E. coli bacteria after 104 minutes would be approximately 4.42 x 10¹⁰.

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a) Monthly instalments = $141.90, calculated using the present value of an annuity formula and 1.25% monthly interest rate.

b) Total cost of buying the laptop on HP = $2172.80, including the deposit amount and total instalments paid over the 12-month period.

a) The deposit amount is $1850 x 20% = $370. The remaining balance to be paid is $1850 - $370 = $1480. The interest rate charged per month is 15%/12 = 1.25%. Using the formula for the present value of an annuity, the monthly instalments can be calculated as $141.90 (rounded to the nearest cent).

b) The total cost of buying the laptop on HP can be calculated by adding the deposit amount to the total amount paid over the 12-month period. Therefore, the total cost is $370 + ($141.90 x 12) = $2172.80.

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Answer:

\(\frac{1}{a} =\frac{1}{b} +\frac{1}{c} \\ \\\frac{1}{a} = \frac{1}{3} + \frac{1}{2/3} \\\\\frac{1}{a} = \frac{1}{3} + \frac{3}{2}\\\\\frac{1}{a} = \frac{11}{6}\\\\a = \frac{6}{11}\)

The amount of water that should be mixed with 18 liters of 14% bleach solution to form 10% bleach solution is 7.2 liters.

The amount of water should be mixed with 1 liter of 14% bleach solution,

we know that the water will have 0% bleach. thus, the amount of water we need to mix with the 14% bleach solution is (2/5) liters.

Therefore, the ratio of water and bleach solution can be written as,

\(\rm \dfrac{14\%\ solution}{Water} = \dfrac{5}{2}\)

We know the ratio of water and bleach solution that should be mixed to form a 10% concentration bleach is (5/2), therefore, we will use the same ratio,

\(\rm \dfrac{14\%\ solution}{Water} = \dfrac{5}{2}\)

\(\rm \dfrac{18}{Water} = \dfrac{5}{2}\\\\\rm {Water} = \dfrac{18\times 2}{5}\\\\\rm Water = 7.2\ liters\)

Hence, the amount of water that should be mixed with 18 liters of 14% bleach solution to form 10% bleach solution is 7.2 liters.

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The null hypothesis would be that the population proportion of those who like the taste of beer is 55%

To determine the expected frequency values for this study, we need to use the given population proportion of 55% and the sample size of 200 people. The expected frequency for those who like the taste of beer would be 55% of the sample size, which is 0.55 x 200 = 110. The expected frequency for those who do not like the taste of beer would be 45% of the sample size, which is 0.45 x 200 = 90.

Expected frequency values are the predicted number of observations in a given category based on the assumption that the population proportion is true. In hypothesis testing, we use these expected frequency values to calculate the chi-square statistic, which helps us determine whether the observed data deviates significantly from what we would expect if the null hypothesis were true.

In this case, the null hypothesis would be that the population proportion of those who like the taste of beer is 55%. If the observed data significantly deviates from our expected frequency values, we may reject the null hypothesis and conclude that the population proportion is not 55%.

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A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. So the correct answer is option B.

inequality the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

We can start by dividing the inequality by 3 to get ...

 8 -4x < 2(x -5)

And we can divide by 2 to simplify further to ...

 4 -2x < x -5

Now, we can add 2x+5, which gives ...

 9 < 3x

and then divide by 3 again:

 3 < x

Therefore number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. So the correct answer is option B.

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We are asked to find the values needed for the length CB

The coordinates of points C and B are given as

C(-a, -5b)

Recall that the distance formula is given by

For the given case,

Let us substitute these coordinates into the above distance formula

Therefore, the required values are

The magnitude of vector A of the following components AX and AY is 88.95m

In this question we will apply the pythagoras theorem which will be depicted as

\(R = \sqrt{AX^{2} + AY^{2} }\) . . . . . . . . . (1)

where , R = resultant magnitude of vector

            AX and AY are the components of vector

As per the question

AX = 83m

AY = 32m

Putting the values in the equation (1) we get

                               \(R= \sqrt{83^{2} +32^{2} }\)

                               \(R =\sqrt{6889+1024}\)

                               \(R=\sqrt{7913}\\\)

                               R  =  88.95m

Thus the magnitude of vector A for the following components is 88.95m

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Answer:

C

Step-by-step explanation:

Remember that we can use the discriminant to determine the amount of roots that a quadratic function has.

If the determinant equals 0, then we only have one real root.

Our function is given by:

\(f(x)=x^2+bx+9\)

Then the discriminant will be:

\(\Delta = b^2-4(1)(9)=b^2-36\)

We only have one real root, thus our discriminant must be 0:

\(0=b^2-36\)

Solve for b:

\(b^2=36\)

Thus:

\(b=\pm 6\)

The answer is both II and III.

The final answer, then, is C.

The integral diverges, the integral converges if the function being integrated approaches 0 as the upper limit approaches infinity.

In this case, the function f(x)=−4(x+4)

2

 does not approach 0 as x approaches infinity. In fact, it approaches negative infinity. This means that the integral diverges.

Here is a Python code that shows how to evaluate the integral:

Python

import math

def integral(x):

 return -4 * (x + 4) ** 3 / 3

print(integral(100))

The output of this code is -1499818.6666666667. This shows that the integral does not converge to a specific value. Instead, it approaches negative infinity as the upper limit approaches infinity.

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After 3 years the rate of motorcycle be Rs. 17520458 when its price is depreciated per year by 8%.

Let after x years the price of the motor cycle be Rs 175204.58

According to the given question.

The present price of a motorcycle is Rs. 225000.

And the depreciation rate = 8% = 0.08.

Therefore, the numbers of years after which the price of motorcycle be Rs 175204.58 is gievn by

⇒ 175204.58  = 225000(1 - 0.08)^x

⇒ 175204.58/225000 = (1 - 0.08)^x

⇒ 0.78 = (1 -0.08)^x

⇒ 0.78 = 0.92^x

⇒ -0.107 = xlog(0.92)

⇒ -0.107 = x(-0.036)

⇒ 0.107/0.036 = x

⇒ x = 2.97

⇒ x ≈ 3 years

Hence, after 3 years the rate of motorcycle be Rs. 17520458 when its price is depreciated per year by 8%.

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To calculate the probability of a major flood occurring exactly once in the next 11 years, we need to make assumptions about the probability of a major flood in a given year. Let's assume that the probability of a major flood in any given year is constant and equal to p.

The probability of a major flood occurring exactly once in the next 11 years can be calculated using the binomial probability formula:

P(X = k) = (nCk) * p^k * (1 - p)^(n - k)

In this case, we have n = 11 (the number of years) and k = 1 (the number of major floods we want to occur). We need to determine the value of p to calculate the probability.

Without specific information about the probability of a major flood in a year, we cannot provide an exact answer. However, if we assume a certain probability value for a major flood in a year, we can calculate the probability using the formula above.

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There were 16 ounces of oil in the lantern at noon.

Let's start by defining the variables we know. We'll call the amount of oil in the lantern at noon "x," the rate at which the oil burns "r," and the time elapsed from noon to 2 pm "t." We know that the amount of oil in the lantern at 2 pm is 12 ounces, and at 4 pm, it's 8 ounces.

We can use the rate of oil burning to create an equation relating the amount of oil in the lantern to the time elapsed. The equation is:

x - rt = y

where "y" is the amount of oil in the lantern at any given time after noon. We can solve for "x" by plugging in the values we know at 2 pm:

x - 2r = 12

And at 4 pm:

x - 4r = 8

Now we have two equations with two variables. We can solve for "r" by subtracting the second equation from the first:

2r = 4

r = 2

Now we can plug in "r" to one of the equations to solve for "x." Let's use the first equation:

x - 2(2) = 12

x - 4 = 12

x = 16

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Answer:

binomial

Step-by-step explanation:

2 terms

Answer:

binomial

Step-by-step explanation:

2 terms (-2.5x^2y) and (-4). when different variables are being multiplied in that form, they are considered as 1 term.