Please help with this SAT question. A solution gets Brainliest!

Answer:

Step-by-step explanation:

This distance can be calculated by using the distance formula. The distance between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) can be defined as d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 .Jun 2, 2017

Answer:

9/5 or 1 \(\frac{4}{5}\)

Step-by-step explanation:

when multiplying a whole number and a fraction, a fun trick i learned is multiply by the top and divide by the bottom.

3·3=9

9÷5=\(\frac{9}{5}\)

as an improper fraction it would be

1 \(\frac{4}{5}\)

Plz mark as brainliest and rate if i was correct.

Answer:

\(\frac{9}{5}\)

Step-by-step explanation:

3 * 3/5

~Make the 3 improper fraction (note that you can make any whole number a fraction if you put a 1 as the denominator)

3/1 * 3/5

~Multiply both numerators and denominators

9/5

Best of Luck!

The length of the sides of the triangle in discuss as required are; 28 in., 16 in., and 10 in.

It follows from the task content that the length of the sides of the triangle as described are to be determined.

Let the longest side be; x

The medium side be; x - 12

The smallest side be; (x - 12) - 6.

Therefore, since the perimeter is the sum of all side lengths;

x + x - 12 + x - 12 - 6 = 54

3x = 84

x = 28

Therefore, the longer side is; 28 in.

The medium side is; 28 - 12 = 16 in.

The shortest side is; 16 - 6 = 10 in.

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The value of the function, f(1) is 3. Note that the answer is already in its simplest form and cannot be expressed as a fraction.

First, let's start by understanding what the function f(x) represents. The function f(x) takes an input value x and returns an output value based on a specific rule. In this case, the rule is defined by the equation f(x) = 4(1/4)^x+2.

To find f(1), we need to substitute 1 in place of x in the equation for f(x). So, we get:

f(1) = 4(1/4)^1 + 2

Now, we need to simplify this expression. Recall that any number raised to the power of 1 is just that number itself. So, (1/4)^1 is just 1/4.

Therefore, we can simplify the expression as follows:

f(1) = 4(1/4) + 2

= 1 + 2

= 3

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By examining a scatterplot, you can gain valuable insights into the relationship between the two quantitative variables x and y, such as direction, strength, form, and outliers.

From examining a scatterplot of two quantitative variables x and y, you can observe the following features about the relationship between the variables:

1. Direction: You can determine whether the relationship between the variables is positive (both variables tend to increase or decrease together) or negative (one variable tends to increase while the other tends to decrease).

2. Strength: You can assess the strength of the relationship by observing how closely the data points are clustered around an imaginary line (e.g., a straight or curved line). A strong relationship has points closely clustered, while a weak relationship has points more scattered.

3. Form: You can identify the form of the relationship, such as linear (points form a straight line) or nonlinear (points form a curve).

4. Outliers: You can detect any outliers, which are data points that do not follow the general pattern of the relationship between the variables.

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Answer:

 . .

Step-by-step explanation:;

To find the absolute maximum value of the function g(x)=−2x^2/x−1 over the closed interval [−3,5], we will use the Extreme Value Theorem (EVT).EVT states that if a function is continuous over a closed interval, then the function will have an absolute maximum and minimum over that interval.

So, for finding the absolute maximum value of the given function, we will follow these steps:Step 1: Check the function's domain.We know that the denominator of the function g(x) is x - 1, so the function is not defined at x = 1. However, the closed interval we are working with is [-3, 5], which does not include x = 1. Hence, the function is defined over this interval.Step 2: Find the critical points of the functionTo find the critical points, we need to differentiate the function g(x) and equate it to zero:g'(x) = (-4x(x-1) + 2x^2)/(x-1)^2= 2x(3-x)/(x-1)^2=0So, the critical points of g(x) are x = 0 and x = 3.Step 3: Find the end-point values of the functiong(-3) = -2/5, g(5) = -50/9.

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The volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\) To find the volume when the area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we can use the method of cylindrical shells.

First, let's find the points of intersection between the two curves by setting them equal to each other:

\(\[x^2 = \frac{3}{x^3}\]\)

To simplify this equation, we can multiply both sides by \(\(x^3\)\):

\(\[x^5 = 3\]\)

Now, taking the fifth root of both sides:

\(\[x = \sqrt[5]{3}\]\)

So the two curves intersect at \(\(x = \sqrt[5]{3}\)\).

To calculate the volume area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we need to integrate the circumference of each cylindrical shell multiplied by its height. The height of each shell is the difference in the y-values of the two curves, and the circumference is\(\(2\pi x\)\).

Let's integrate from \(\(x = 0\)\) to \(\(x = \sqrt[5]{3}\)\):

\(\[V = \int_0^{\sqrt[5]{3}} 2\pi x \left(\frac{3}{x^3} - x^2\right) \, dx\]\)

Simplifying this expression:

\(\[V = 2\pi \int_0^{\sqrt[5]{3}} \left(\frac{3}{x} - x^3\right) \, dx\]\)

Integrating each term separately:

\(\[V = 2\pi \left[3 \ln|x| - \frac{x^4}{4}\right]_0^{\sqrt[5]{3}}\]\)

Plugging in the limits of integration:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right] - 2\pi \left[3 \ln|0| - \frac{0^4}{4}\right]\]\)

Since \(\(\ln|0|\)\)is undefined, the second term on the right side is zero:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right]\]\)

Simplifying further:

\(\[V = 2\pi \left[3 \ln 3^{\frac{1}{5}} - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

Using the properties of logarithms, we can simplify the first term:

\(\[V = 2\pi \left[3 \cdot \frac{1}{5} \ln 3 - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

\(\[V = \frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\]\)

So the volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\)

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a) The plane must descend about 19,860.58 feet to pass over the tower.  b)  To fly 1000 feet above the tower, the plane must fly at an altitude of 1139.42 feet.

a) To find the height of the tower, we can use the tangent function in trigonometry.

Let's call the height of the tower "h".

We know that:

tan(1°) = h / 25000

Solving for h, we get:

h = 25000 * tan(1°)

Using a calculator, we find that:

h ≈ 139.42 feet

So the tower is about 139.42 feet tall.

To pass over the tower, the plane must rise an additional 139.42 - 20,000 = -19,860.58 feet.

That is, the plane must descend about 19,860.58 feet to pass over the tower.

b) To fly 1000 feet above the tower,

The plane must fly at an altitude of 139.42 + 1000 = 1139.42 feet.

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The statement 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value' is True.

In this question, we have been given a statement - 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.'

We need to state whether it is true or false.

We know that, the minimum value of the objective function Z = ax + by in a linear programming problem can also occur at more than one corner points of the feasible region.

Therefore, when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.

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Answer:

60°

Step-by-step explanation:

each interior angle of a regular hexagon measures 120° (720° divided by 6 sides)

therefore, each exterior angle measures 180-120 = 60°

If each driver’s distance (miles) is shown for the same elapsed time (hours) of the trip. The person that had a head start is: Rita had a 28-mile head start.

Slope for speed = (y² - y1) / (x² - x1)

Slope for speed = (130 - 65) / (2 - 1)

Slope for speed= 65 / 1

Slope for speed= 65 mph

Determining Roger's starting position if Roger distance is 65.

Hence,

Mile of head start = Slope of speed - Roger distance

Mile of head start = 65 mph - 65 miles

Mile of head start = 0 miles

Rita  starting position if Rita distance is 93

Slope for speed = (y² - y1) / (x² - x1)

Slope for speed = (158 - 93) / (2 - 1)

Slope for speed = 65 / 1

Slope for speed = 65 mph  

Mile of head start = Slope of speed - Rita distance

Mile of head start =  93 - 65

Mile of head start= 28 miles

Therefore we can conclude that Rita has a head start of 28 miles.

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Answer:

Rita had a 28-mile head start.

Step-by-step explanation:

EDGE

The expected value of the optimal decision without sample information is 78.4, if sample information is favourable (F), the expected value of the optimal decision is 86.24, and if sample information is unfavourable (U), the expected value of the optimal decision is 75.52.

Given information: P(s1) = 0.56P(s1) = 0.56P(F|s1) = 0.66P(F|s1) = 0.66P(U|s2) = 0.68P(U|s2) = 0.68

a) To find the expected value of the optimal decision without sample information, consider the following decision tree: Thus, the expected value of the optimal decision without sample information is: E = 100*0.44 + 70*0.56 = 78.4

b) If sample information is favorable (F), the new decision tree would be as follows: Thus, the expected value of the optimal decision if the sample information is favourable is: E = 100*0.44*0.34 + 140*0.44*0.66 + 70*0.56*0.34 + 40*0.56*0.66 = 86.24

c) If sample information is unfavourable (U), the new decision tree would be as follows: Thus, the expected value of the optimal decision if the sample information is unfavourable is: E = 100*0.44*0.32 + 70*0.44*0.68 + 140*0.56*0.32 + 40*0.56*0.68 = 75.52

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Answer:

-----------------------

Using the formula for the union of two sets:

where

We are given that:

Plugging in the values, we get:

Therefore, set B contains 42 elements.

The correct answer is: d. Yes, the probability of a random ladybug in Raleigh being bigger than 1.5 cm and it is appropriate to calculate this probability.

It is appropriate to use a normal distribution to approximate the distribution of ladybug lengths since the sample size is large enough (440000) and the standard deviation is known. We can calculate the z-score for a ladybug with length of 1.5 cm as:

z = (1.5 - 1) / 0.2 = 2.5

Using a standard normal distribution table, we can find the probability of a z-score being greater than 2.5 to be approximately 0.0062. Therefore, the probability of a random ladybug in Raleigh being bigger than 1.5 cm is about 0.0062 or 0.62%.

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The correct option regarding the numeric values of the functions at x = -3 is given as follows:

f(-3) < g(-3).

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

At x = -3, the definition of function f(x) for this problem is given as follows:

f(x) = 3x + 4.

(piece-wise function has different definitions depending on the input, -3 is less than 1 hence the first definition is applied).

Hence the numeric value is:

f(-3) = 3(-3) + 4 = -9 + 4 = -5.

From the table, the numeric value of function g(x) at x = -3 is given as follows:

g(-3) = 0.

0 is greater than -5, hence the correct option is given as follows:

f(-3) < g(-3).

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Let x be the amount invested in the 5-yr CD and y be the amount invested in the 18-month CD.

We have the following equations:

0.044x + 0.03(x - 2000) = 1102.50 (total interest equation)

x + (x - 2000) = Total amount invested

Solving this system of equations will give the values of x and y

To determine how much was invested in each CD, we can set up a system of equations. Let x represent the amount invested in the 5-yr CD and y represent the amount invested in the 18-month CD.

The interest earned from the 5-yr CD can be calculated using the formula I = Prt, where I is the interest, P is the principal (amount invested), r is the interest rate, and t is the time in years. In this case, the interest equation for the 5-yr CD is 0.044x.

The interest earned from the 18-month CD can be calculated in the same way, using the formula I = Prt. However, since the time is given in months, we need to convert it to years by dividing by 12. The interest equation for the 18-month CD is 0.03(x - 2000).

The total interest earned from both CDs is $1102.50, so we have the equation 0.044x + 0.03(x - 2000) = 1102.50.

Additionally, the total amount invested is the sum of the amounts invested in each CD, which is x + (x - 2000).

By solving this system of equations, we can determine the values of x and y, representing the amounts invested in each CD. The solution to the system will provide the specific amounts invested in the 5-yr CD and the 18-month CD.

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The distance traveled by a particle with position (x, y) as t varies in a given time interval can be determined by integrating the speed of the particle with respect to time over that interval. This integration involves calculating the derivatives of x and y with respect to t, representing the rates of change in the x and y coordinates over time. By integrating the speed function, we obtain the total distance traveled by the particle within the given time interval.

To compare this distance with the length of the curve, we need to consider the curve traced by the particle's path in the (x, y) plane. The length of the curve represents the total distance along the curve, taking into account its shape and curvature. Comparing the distance traveled by the particle with the length of the curve allows us to assess if the particle deviates from a straight path or follows a more complex trajectory, providing insights into the particle's motion characteristics.

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The distance traveled by a particle with position (x, y) as t varies in a given time interval, we need to integrate the speed of the particle with respect to time over that interval. This will give us the length of the curve traced by the particle's position.

The distance traveled by a particle is determined by integrating its speed over a given time interval. The speed of the particle is the magnitude of its velocity, which can be calculated using the derivatives of the position function.

Let's assume the particle's position is given by a parametric equation x = f(t) and y = g(t), where t represents time. The velocity of the particle can be found by taking the derivatives of f(t) and g(t) with respect to t.

The speed of the particle is then calculated as the magnitude of the velocity vector, which is the square root of the sum of the squares of the derivatives: sqrt((dx/dt)^2 + (dy/dt)^2).

To find the distance traveled by the particle over a specific time interval, we integrate the speed function over that interval with respect to t. This will give us the length of the curve traced by the particle's position.

In summary, to find the distance traveled by a particle, we calculate the speed as the magnitude of its velocity and integrate the speed function over the given time interval. The result will be the length of the curve traced by the particle's position.

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Answer:

-2x - 2

Step-by-step explanation:

Step 1: Write expression

3 - (2x + 5)

Step 2: Distribute negative

3 - 2x - 5

Step 3: Combine like terms

-2x - 2

Answer:

elsa can do 150 in 3 minutes.

so together they can do 450 in 3 minutes, or 150 in 1 minute

they would need two minutes

Answer:

4.5 minutes long to do their job.

Answer:

50 kg of green tea leaves and 50 kg of assam black tea leaves.

Step-by-step explanation:

Let x kg be the amount of green tea and y kg be the amount of Assam tea.

x+y=100 (1) [mass]

price for 1 kg of assam tea= 7.20/600×1000g

= $12/kg

total cost= 100×10

= $1000

8x+12y= 1000 (2) [cost]

(1)×8: 8x+8y= 800 (3)

(2)-(3): (8x+12y)-(8x+8y)= 1000-800

4y= 200

y= 50 (4)

sub (4) into (1):

x+50= 100

x= 50

Answer: the large jar is cheaper

Step-by-step explanation:

If you divide the £1.54 by 440g and £1.26 by 340g, you'll find which one is cheaper per gram :

1.54/440 = 0.0035

1.26/340 = 0.0037

So, by comparing both prices/gram, you've found that the large jar is cheaper.

The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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\(\boxed{275.67+3(16.32)+24.39+27.40x \leq 560}\\\\27.40x +349.02 \leq 560\\\\27.40x \leq 210.98\\\\x \leq 7.7\)

Rounding down yields \(\boxed{x \leq 7}\).

Answer:

Step-by-step explanation:

560

Answer:

72

Step-by-step explanation:

volume = l x w x h

4 x 3 x 6

Answer:

Zeke will receive $2.75.

Step-by-step explanation:

Helmet cost: (3/5) x 28.75 = $17.25

Gives = $20

20 - 17.25 = 2.75

Original question:

Zeke goes to a skate shop with his friend Tristan. Tristan buys a helmet that costs $28.75. Zeke finds a helmet that is (3/5) of the cost of Tristan's helmet. If Zeke gives the cashier a $20 bill, how much change will he receive?

Answer:

The amount of money originally invested which is the principal P = 5,000

Step-by-step explanation:

Using the compound interest formula, the return on investment can be represented on the interest function as;

f(x) = P(1+r)^x

Where

P is the principal which is the initial investment.

r = rate Proportion

x = time (number of years)

Comparing to the given function;

f(x) = 5,000(1 + 0.04)^x

We can see that;

Principal P = 5,000

Rate r = 0.04

time = x

The amount of money originally invested which is the principal P = 5,000

Answer:

Following are the solution to this question:

Step-by-step explanation:

For incentive A

The car value = 57000

Calculating debt\(= 57000 - 10000\)

                            \(= 47000\)

Calculating the debt value after incentive \(= 47000 - 5000\)

                                                                    \(= 42000\)

\(PMT = \frac{P(\frac{r}{n})}{(1 - (1 + (\frac{r}{n}))^(-nt))}\)

         \(= \frac{42000 \times (\frac{6.06 \%}{12})}{(1-(1+(\frac{6.06 \%}{12}))^{(-12 \times 4)})}\)

         \(= \frac{42000 \times (0.00505)}{(1-(1+(0.00505))^{(-48)})}\\\\= \frac{212.1}{(1-(1+(0.00505))^{(-48)})}\\\\=\frac{212.1}{-1.74}\\\\= - 121.89 \ \ or \ \ 121.89\)

For incentive  B

The car value = 57000

Calculating the debt value \(= 57000 - 10000\)

                                            \(= 47000\)

Calculating the monthly payment =\(\frac{47000}{(12*4)}\)

                                                        \(= \frac{47000}{(48)}\\\\= \frac{47000}{(48)}\\\\=979.166\)

difference:

\(=121.89 - 979.166\\\\ = - 854.276\)