If the gradient of the line joining (4, a) and (7, 5) is 2. Find the value of a.

Answer:

y=2

Step-by-step explanation:

3x+4y=20

3*4+4y=20

12+4y=20

4y=20-12

4y=8

y=8/4

y=2

Step-by-step explanation:

The answer is 2, 3*4= 12 and 4*2=8. if you add both of them you get 20.

Answer:

There is a correlation between amount of bread bought and amount of rice purchased. However, there is no causation. This is because there is an increase in the amount of rice purchased with a decrease in the amount of bread bought.

Step-by-step explanation:

We see that there is a correlation between the amount of bread and the amount of rice bought .

When the bread is bought the amount of rice drops and when the amount of bread is decreased the amount of rice increases.

There is no causation meaning there is no direct affect of buying more bread or rice.Buying of rice does not directly cause the purchase of bread.

Hence there is correlation but not causation.

Correlation and causation can occur at the same time when one event causes the other.

Answer:

−1 27/80

Step-by-step explanation:

Answer:

The chances are very high because there are more nickels then there quarters, dimes, and pennies.

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

\((m - n) \: (m - n)\)

\(m { \: }^{2} - mn - mn + n {}^{2} \)

\(m {}^{2} + n {}^{2} \)

the mn has been cancelled and it's now zero

Answer:

47.9

Step-by-step explanation:

Call the number "x"

As per the problem,

2 ( x + 2 ) = 99.8

Inverse operations

2 ( x + 2 ) = 99.8

/2              /2

x + 2 = 49.9

-2        -2

x = 47.9

Answer: answer for a is 690 and answer for b is 3910

Step-by-step explanation:

for first you times 4600 by .15 and than you get and than you subtract 690 from 4600.

Answer:

The numbers are 10 and 21.

Step-by-step explanation:

x + y = 31

xy = 210

x = 31 - y

(31 - y)y = 210

31y - y² = 210

y² - 31y + 210 = 0

(y - 21)(y - 10) = 0

y - 21 = 0  or  y - 10 = 0

y = 21  or  y = 10

The two real numbers are 10 and 21.

Quadratic Equations are algebraic expressions of degree 2 in one variable and are of the form ax² + bx + c = 0.

In simpler terms, a quadratic equation is be defined as a polynomial equation of degree 2.

Given that, there are two real numbers with a sum of 31 and a product of 210.

We need to find their values using the concept of quadratic equation,

So, according to the question,

x + y = 31 (eq 1)

xy = 210 (eq 2)

x = 31 - y

(31 - y) y = 210

31y - y² = 210

y² - 31y + 210 = 0

(y - 21) (y - 10) = 0

y - 21 = 0 or y - 10 = 0

y = 21 or y = 10

Hence, the two real numbers are 10 and 21.

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The required solution to the given inequality is x < 7/4.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given that,
To determine the simplified solution of the inequality 1/2x−1/4 < 5/8.
1/2x−1/4<5/8 .

Adding 1/4 on both sides of the equality,

1/2x < 5 / 8 + 1 / 4
Multiply by 2 on both sides of equality,
1 / 2x < 7 / 8
x < 7 / 4

So, the solution of inequality lies x greater than 7/4, as of the given conditions.

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Answer:

3rd option down

Step-by-step explanation:

Simplify the inequality and you should get this:

-48\(\leq\)-5x+2<-18  

-2 .     -2 .       -2

-50\(\leq\)-5x<-20

Divide by -5

Remember to switch places since we are dividing by a negative number

You should get this 4\(\leq\)x<10

The only number line that shows that properly would be the 3rd one down.  

Answer:

c

Step-by-step explanation:

The total number of pairs sold by SoccerWorld is 57

From the question, we have the following parameters that can be used in our computation:

The above parameters means that

s = 3j

d = 5 + j

70(s + d + j) = 7000

Where

j = JP Sports

s = SoccerWorld

d = DirectSportz

Divide both sides of 70(s + d + j) = 7000 by 70

s + d + j = 100

Substitute s = 3j and d = 5 + j

3j + 5 + j + j = 100

Evaluate the like terms

5j = 95

Divide by 5

j = 19

Substitute j = 19 in s = 3j

s = 3 * 19

So, we have

s = 57

Hence, the number of pairs is 57

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If Aaron is designing a party game in which he needs exactly 24 possible outcomes, then he can use the following sets of actions to have a statistically fair game from the Statistics point  of view,

Toss a coin twice, and then then roll a 6-sided number cube.

How can he play a statistically fair game to get exactly 24 outcomes?

The game has 24 alternative outcomes, as far as we know. The next step is to identify a series of activities that produces 24 distinct outcomes with equal probabilities.

The first of the alternatives is the only one with a sample space of 24 elements.

Flip two coins, then roll a D6.

The results of each coin toss are 2:  (tails and heads).

There are 6 outcomes for the D6: (1, 2, 3, 4, 5, 6)

The combined outcomes of the two throws and rolling the number are then given by the product between the numbers of outcomes for each individual part, as solved below:

C = 2 × 2 × 6

C = 24

Thus, by tossing a coin twice, and then then rolling a 6-sided number cube, Aron can play a statistically fair game if h needs exactly 24 outcomes.

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Answer:

B.

Step-by-step explanation:

V = (pi)r^2h

V = 3.14 * (8 m)^2 * 28 m

V = 5626.9 m^3

Answer: B.

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

No, it does not matter who will go first as the probability of getting both head and tail after flipping a coin is equal to ( 1 / 2 ).

As given in the question,

Number of players playing the game = 2

Number of coins to flip = One

Possible outcomes after flipping a coin = { Head , Coin }

Probability of getting a head

= (Number of favourable outcomes) / ( Total number of outcomes)

= 1 / 2

Probability of getting a tail

= 1 / 2

Either you tossed first or second chances are fifty percent.

Therefore, it does not matter who will go first as probability of getting head and tail is ( 1 / 2) after flipping a coin.

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Answer:

Step-by-step explanation:

(-5 + 2)/(4 + 2) = -3/6 = -1/2

y + 2 = -1/2(x + 2)

y + 2 = -1/2x - 1

y = -1/2x - 3

Answer: y= -1/2x -3

Step-by-step explanation: you just have to do -5- (-2) over 4-(-2) when u divide these two you should get the slope. When you get the slope pick one of the coordinates in your questions and plug them in as Mx + b form.

Answer:

dont know sorryyyyyyyyyy

Answer:

A(3,-1) and B( -2,1)

Step-by-step explanation:

2x+5y=1. , or. y=(1–2x)/5………….(1)

x^2+5xy-4y^2+10=0…………………..(2)

Putting y=(1–2x)/5 from eqn. (1)

x^2+5x.(1–2x)/5–4/25.(1–2x)^2 +10=0

or. 25x^2+25x.(1–2x)-4.(1+4x^2–4x)+250 = 0

or. 25x^2+25x-50x^2–4–16x^2+16x+250=0

or. 41x^2–41x-246=0

or x^2– x - 6=0

or. (x-3).(x+2)=0

x= 3 or -2

But y=(1–2x)/5

y= (1–6)/5 or. (1+4)/5

y= -1. or. 1

The interest rate is 10.89%

1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..

The size of the nominal money supply in the new short-run equilibrium is 121.07.

2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.

Real exchange rate will remain unchanged.

3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.

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Answer:

One possible equation is  2m+16 = 40

There are other possible equations to set up as well.

That equation solves to m = 12 which means both plans cost the same when you go 12 MB over the limit (using 27 MB total).

===============================================================

Explanation:

The unlimited plan costs $40 a month no matter how much data you use.

The second plan costs $16 a month, and there are no extra fees as long as you don't go over the limit of 15 MB. If you do exceed this limit, then you're charged an extra $2 per MB. That means an extra 2m dollars is tacked onto the 16 mentioned earlier,  where m is the amount of MB you've gone over the limit. Overall, the expression 2m+16 represents the cost of the second plan. If you don't go over the limit, then you'll use m = 0 for the second plan.

Set that expression equal to 40 to set up the equation. Solving the equation leads to...

2m+16 = 40

2m = 40-16

2m = 24

m = 24/2

m = 12

If you exceed the limit by 12 MB, then both plans cost the same at $40 per month.

Note: Going 12 MB over the limit means you've used 15+12 = 27 MB.

The expected one-period return for the asset is given by the expression 0.0675 + 0.045 + 0.03 + 0.04p + 0.04, where 'p' represents an unknown probability.

The given probability distribution represents the one-period return for an asset, with corresponding probabilities assigned to each return value. To find the expected one-period return, we need to calculate the weighted average of the returns, where the weights are the probabilities.

Let's calculate the expected one-period return step by step:

1. Multiply each return value by its corresponding probability:

  0.27 * 0.25 = 0.0675

  0.18 * 0.25 = 0.045

  0.10 * 0.30 = 0.03

  p * 0.04 = 0.04p

  0.20 * 0.20 = 0.04

2. Sum up the products calculated in step 1:

  0.0675 + 0.045 + 0.03 + 0.04p + 0.04

3. Set the sum equal to the expected one-period return, denoted as E(R):

  E(R) = 0.0675 + 0.045 + 0.03 + 0.04p + 0.04

Therefore, the expected one-period return of the asset is 0.0675 + 0.045 + 0.03 + 0.04p + 0.04.

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The probability that Robert is approved on both the written application and the interview is approximately 0.5531

To find the probability that Robert is approved on both the written application and the interview, we can use the formula for conditional probability

P(A and B) = P(B | A) × P(A)

where A and B are events, P(A) is the probability of event A, and P(B | A) is the probability of event B given that event A has occurred.

Let's define the events

A = "Robert is approved on the written application"

B = "Robert is approved by the interview committee"

We know that P(A) = 0.67, and P(B | A) = 0.83. We want to find P(A and B), which represents the probability that both events A and B occur.

Using the formula for conditional probability, we have

P(A and B) = P(B | A) × P(A)

P(A and B) = 0.83 × 0.67

P(A and B) = 0.5531

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ANSWER :- slope =0

Hipe this will help

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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The same well-liked crackers are discounted at Value Grocery Mart and Market City are 5.25, 10.5,  15.75, and 21.

As the cost per pack is C=1.75b. C is the Cost in dollars.

3×1.75=5.25

6×1.75=10.5

9×1.75=15.75

12×1.75=21

An example of a chart is one that uses symbols to depict the data, such as bars in a bar chart, columns in a line chart, or slices in a pie chart.  A chart can convey various information by representing tabular numerical data, functions, or certain types of quality structures.

Users can change numerous rows and columns in a table at once using a tabular form and a single page.

A chart displays data that can be shown as a table, graph, or diagram. There are different ways to convey vast amounts of information in it.

Here, the table is.

Number of Boxes of Crackers ║   Grocery Mart  ║    Market City:

  3                                              ║       5                  ║  5.25

 6                                                ║     10                   ║ 10.5

 9                                                ║      15                   ║ 15.75

 12                                              ║      20                    ║ 21

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Answer:  There is a total of 900 seats in the auditorium.

Step-by-step explanation:

there is a formula for this

t - n = a + ( n - 1) d

It is called a Arithmetic Progression.

We use this to find the number of seats in the last row first.

a = initial value, 12

d = common difference for each successive term

n = is the number of terms in the sequence

t - 25 = 12 + (25 -1) * 2

We ignore the left side for now, just solve the right and we get 60.

Now we use the equation,

n / 2 (2a + n -1 * d)

So,

25/2 ( 24 + 24 * d)

The answer is 900

a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.

b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.

a) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.

b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.

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Answer:

49 Hours

Step-by-step explanation:

If it takes him 1 hour to finish 1 page of notes and he already finished 1, he would need to do a total of 49 hours to get 49 more pages done.

Hope this helps!

The price of organic sugar was decreased by 25%, which means the new price is 75% of the original price. To find the new price of the sugar, we can multiply the original price by 0.75:

New price = $4 * 0.75 = $3

Therefore, the new price of the organic sugar is $3 per pound.

Answer:

3.7

Step-by-step explanation:

The lenght of an arc with a radius of 3m and substended angle of 70 degrees is 3.7meters

The length of an arc is expressed as:

L = r theta

Given the following parameters

r = 3m

theta = 70 degrees = 70π/180

L = 3(70π/180)

L = 3.7 metres

Hence the lenght of an arc is 3.7meters

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