what's the function for this table? :(

Answer:

Sum= addition

lets set the problem up like this

and let the first number equal A and the second number is B

This what we know:

14 = (a ) + 2(B)

A - B = 2

We need to find A and B

Step-by-step explanation:

Answer:

m = - 7

Step-by-step explanation:

Given

6(m - 1) = 3(3m + 5) ← distribute parenthesis on both sides

6m - 6 = 9m + 15 ( subtract 9m from both sides )

- 3m - 6 = 15 ( add 6 to both sides )

- 3m = 21 ( divide both sides by - 3 )

m = - 7

Answer:

8 minutes

Step-by-step explanation:

Since the level of the tank needs to be at two-thirds its original level, then this means that Andrew needs to drain only one-third of the fish tank. Therefore the amount of time it would take can easily be solved with this 2-step equation...

6t = 144 * [tex]\frac{1}{3}[/tex] .... first multiply the right side of the equation

6t = 48   ... next divide both sides by 6

t = 8

Finally, we can see that it will take Andrew 8 minutes to drain the tank to two-thirds of its original level.

The linear approximation for g(x) = ∛(1+x) at a = 0 is g(x) = 1 + 0.33x.

The linear approximation of the function g(x) = cube root of 1+x at a = 0 is:

g(x) = 1 + 0.33x

To approximate the cube root of 0.95, we substitute x = -0.05 into the linear approximation. This gives us:

g(-0.05) = 1 + 0.33(-0.05) = 1.0165

Therefore, the cube root of 0.95 is approximately 1.0165.

To approximate the cube root of 1.1, we substitute x = 0.1 into the linear approximation. This gives us:

g(0.1) = 1 + 0.33(0.1) = 1.33

Therefore, the cube root of 1.1 is approximately 1.33.

Note that the linear approximation is only an approximation, and the actual values of the cube roots of 0.95 and 1.1 may be slightly different.

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Answer:

m∠1= 129

m∠2= 18

m∠3= 123

m∠4= 39

Step-by-step explanation:

Let's start off with finding the m∠2 in the triangle.

As you can see, this is a right triangles. So, the measure's of 72 and m∠2 sum up to 90 degrees. The equation would be: 72+m∠2= 90.

Step 1- Subtract 72 to both side.s

72+m∠2= 90

-72             -72

m∠2= 18

Now that we know the measure of m∠2, let's move on to m∠1.

Remember that a triangle always sums up to 180 degrees. So, the equation would be: 72+57+m∠1= 180.

Step 1- Add to simplify.

(72+57)+m∠1= 180

129+m∠1= 180

Step 2- Subtract 129 to both sides.

129+m∠1= 180

-129            -129

m∠1= 129

So, now we know the measure of m∠1. In order to find the m∠3, remember that a straight line always equals 180 degrees. So, the equation would be: 57+m∠3= 180.

Step 1- Subtract 57 to both sides.

57+m∠3= 180

-57               -57

m∠3= 123

Finally, to find the m∠4. As I mentioned earlier, a triangles sums up to 180 degrees. So, the equation would be: 123+18+m∠4= 180.

Step 1- Add to simplify.

(123+18)+m∠4= 180

141+m∠4= 180

Step 2- Subtract 141 to both sides.

141+m∠4= 180

-141             -141

m∠4= 39

Now we know all the measures of the missing angles!

Hope this helped you understand! :)

Answer: a11 + ( b11 + c11 ) = 0

Step-by-step explanation:

A, B, and C represent three matrices of the same size and (A + B) + C = 0.

Answer:

Michelle bought 2 hamburgers and 4 hot dogs

Step-by-step explanation:

As you've already implied, we will need a system of equations to find the amount of hot dogs and hamburgers Michelle bought.

First equation:  We can allow x to represent the number of hot dogs and y the number of hamburgers.  Since she bought 6 items altogether, our first equation is x + y = 6, since:

quantity of hot dogs + quantity of hamburgers = total amount of food

Second equation:  Since she spent $32 altogether, hot dogs cost $5, and hamburgers cost $6, our second equation is 5x + 6y = 32 since:

(price of hot dogs * quantity) + (price of hamburgers* quantity) = total cost.

Method to solve the system:  Substitution:  Isolate x in the first equation and plug it in for x in the second equation to solve for y:

If we isolate x in the first equation, we get x = -y + 6.  

Now we can plug in x = -y + 6 for x in the second equation to first solve for y, the number of hamburgers she bought:

5(-y + 6) + 6y = 32

-5y + 30 + 6y = 32

y + 30 = 32

y = 2

Plug in 2 for y in any of the two equations to solve for x:

We can now plug in 2 for y in the first equation to find x, the number of hot dogs she bought:

x + 2 = 6

x = 4

Thus, Michelle bought 2 hamburgers and 4 hot dogs.

Answer:

Choice B

Step-by-step explanation:

For a triangle to be true, the longest side has to be shorter than the two shorter sides combined. The only answer that fits this is choice be. 70<40+60

Answer:

Yes, he will have $309 during the third week.

Step-by-step explanation:

The first week, he saved $70, then spent $7, subtracting to make $63 left. The next week, he saved $103, then spent $6, subtracting again to leave him with $97. $70 + $97 = $167, which is the current total amount he now has so far. Finally, with $150 earned the third week, but he spends $8 and has $142 leftover, $167 + $142 = $309. Meaning he will exceed by $9 more and will have enough money.

The cost of one banana is 3 cents.Given that Geeta buys x apples, x+7 oranges, and 2 1 x- bananas.The total number of pieces of fruit Geeta buys is 30.

(i) To find the number of apples Geeta buys, we need to form an equation based on the given information.x + x + 7 + 2(1 x-) = 30.Simplify and solve for xx + x + 7 + 2 - 2x = 30-x + 9 = 30x = 30 - 9x = 21.Therefore, the number of apples Geeta buys is 21.

(ii) Cost of 1 apple is 15 cents.Cost of 1 orange is 18 cents.The total cost of all the fruit is $5.55.Cost of 21 apples = 21 × 15 = 315 cents.Cost of (x + 7) oranges = (x + 7) × 18.Cost of 2 1 x- bananas = (2 1 x-) × y cents, where y is the cost of one banana.

Total cost = 315 + (x + 7) × 18 + (2 1 x-) × y= 555 cents.Equating the above equation, we get;315 + (x + 7) × 18 + (2 1 x-) × y= 555315 + 18x + 126 + 2y - 2x - y = 555.

Simplify the equation.16x + y = 114.Now, we need to find the value of y, which is the cost of 1 banana. Given that 21 bananas were already bought, and we need to find the cost of one banana only.

Therefore we need to subtract the cost of 21 bananas from the total cost of all fruit and then divide by the remaining number of bananas.114 - 2 1 x- × y = cost of bananas = (555 - 315 - 18x - 126) cents = 114 cents.Therefore, 2 1 x- × y = 114 - 21 × y y = 3.Hence, the cost of one banana is 3 cents.

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Answer:

5

Step-by-step explanation:

Answer:

The answer is 5

Step-by-step explanation:

We need to find a subset of the vectors v₁ = (0, 2, 2, 4), v₂ = (1, 0, -1, -3), v₃ = (2, 3, 1, 1), and v₄ = (-2, 1, 3, 2) that forms a basis for the space spanned by these vectors. In this problem, we will perform the necessary calculations to determine the subset that forms a basis.

To find a subset of the given vectors that forms a basis for the space spanned by them, we need to check for linear independence among the vectors. We will start by considering all four vectors and then eliminate any redundant vectors.

We can construct an augmented matrix with the given vectors as columns:

[ 0 1 2 -2 ]

[ 2 0 3 1 ]

[ 2 -1 1 3 ]

[ 4 -3 1 2 ]

Applying row operations to the matrix, we can determine if any vectors can be eliminated due to linear dependence. After performing row operations, we find that the matrix is row equivalent to the following matrix:

[ 1 0 0 0 ]

[ 0 1 0 0 ]

[ 0 0 1 0 ]

[ 0 0 0 1 ]

This indicates that all four vectors are linearly independent, and there are no redundant vectors. Therefore, the subset {v₁, v₂, v₃, v₄} forms a basis for the space spanned by these vectors.

Hence, the subset {v₁, v₂, v₃, v₄} is a basis for the space spanned by the given vectors.

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Answer: 2 = x (21+22x = 5+30x)

Step-by-step explanation:

Answer:

52.814 degrees

Step-by-step explanation:

we know that

we have

Convert 51'' to minutes

Convert 48.85' to degrees

Answer:

I don't know if I'm right but I looked it up and found the same picture and it said it was 120

Answer:

300 jumping jacks

Step-by-step explanation:

120 ÷ 2 = 60 jumping jacks per minute

60 × 5 = 300 jumping jacks

Sam can do 300 jumping jacks in 5 minutes.

Hope that helps.

Answer:

60

Step-by-step explanation:

120 / 2 = 60 (jumping jacks per minute)

60 * 5 = 300

Best of Luck!

Answer:

its A

Step-by-step explanation:

i just did this

Answer:

Point T = (4,9)

Step-by-step explanation:

Given:

S (−5,0)

M (10, 15)

m1:m2 = 3:2

Find:

Point T

Computation:

X = [m1x2 + m2x1] / [m1+m2]

Y = [m1y2 + m2y1] / [m1+m2]

X = [(3)(10) + (2)(-5)] / [3+2]

Y = [(3)(15) + (2)(0)] / [3+2]

X = 20 / 5 = 4

Y = 45 / 5 = 9

Point T = (4,9)

Answer:

A: 2t+4

Step-by-step explanation:

Answer:

n=-4

Step-by-step explanation:

First, subtract 3n on both sides. This results in -3=n+1. Then, subtract 1 on both sides. The answer is n=-4.

Answer:

B

Step-by-step explanation:

We have the equation:

[tex]3n-3=4n+1[/tex]

Let's solve for n. To do so, we want to isolate it.

Let's use the subtraction property of equality to subtract 3n from both sides:

[tex](3n-3)-3n=(4n+1)-3n[/tex]

The left side will cancel...

[tex]-3=(4n+1)-3n[/tex]

Subtract on the right:

[tex]-3=1n+1[/tex]

Remember that 1n is the same as just n. So:

[tex]-3=n+1[/tex]

Now, let's use the subtraction property of equality again to subtract 1 from both sides:

[tex](-3)-1=(n+1)-1[/tex]

The right side will cancel. Subtract on the left:

[tex]-4=n[/tex]

Symmetric property:

[tex]n=-4[/tex]

So, our answer is B.

And we're done!

Answer: 1800 Minutes

Step-by-step explanation: 360 x 5 = 1800

Answer:

1800 minutes

Step-by-step explanation:

360×5=1800 minutes.

a. This result is not significant. ; b. we reject the null hypothesis  ; c.The 99% confidence interval for the effect of SmallClass on TestScore is (7.25, 20.55). ; d. The first assumption is plausibly valid for this regression.

a. Yes, small classes have been shown to enhance test scores, as per the analysis carried out. This means that students in smaller classes received an average of 13.9 more points on their tests than those in larger classes.

It is critical to note, however, that this result is not significant.

b. Carry out a test at the 5% level.

The null hypothesis will be H0: β1 = 0.

The alternative hypothesis will be H1: β1 ≠ 0.

This is a two-sided test with a 5% significance level.

Reject the null hypothesis if the t-statistic lies outside the interval (-2.5,2.5).

t-statistic= (13.9-0)/2.5

= 5.56 which is greater than 2.5.

Therefore, we reject the null hypothesis and conclude that the estimated effect of class size on test scores is statistically significant at the 5% level.

c. We know from the regression output that

b1= 13.9,

standard error of b1 (SEb1)= 2.5 and

degrees of freedom (df)= n-2

= 1636-2

= 1634.

The formula for the 99% confidence interval is given by:

Lower limit= 13.9- (2.58*2.5)

= 7.25

Upper limit= 13.9+ (2.58*2.5)

= 20.55

d. Least squares assumption 1 says that the model is linear in parameters.

The regression model

TestScore= 918.0+ 13.9 X

SmallClass is indeed linear in the parameters because we have a first-order linear model.

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9514 1404 393

Answer:

  100°

Step-by-step explanation:

Opposite angles in an inscribed quadrilateral are supplementary:

  x° +80° = 180°

  x° = 100° . . . . . . . subtract 80°

Answer:

2 gallons

Step-by-step explanation:

Answer:

2 gallons for 5.98$

Step-by-step explanation:

for two gallons.

1/4g milk = 12.92

1/2g milk= 8.36

1g milk= 8.50

To write x as the sum of two vectors, one in Span {u₁, u₂, u₃} and one in Span {u₄}, where {u₁, u₂, u₃, u₄} is an orthogonal basis for R⁴, we need to find the components of x that lie in each span.

The vector x can be expressed as a linear combination of u₁, u₂, u₃, and u₄, with the components found by projecting x onto each basis vector.

Given that {u₁, u₂, u₃, u₄} is an orthogonal basis for R⁴, we can express x as the sum of two vectors: one in Span {u₁, u₂, u₃} and one in Span {u₄}. Let's denote the components of x in each span as x₁ and x₂, respectively.

To find x₁, we project x onto the subspace spanned by {u₁, u₂, u₃}. Since {u₁, u₂, u₃} is an orthogonal basis, the projection of x onto each basis vector is given by the dot product of x with the respective basis vector divided by the norm of the basis vector squared. Therefore, we have:

x₁ = (x · u₁) / ||u₁||² + (x · u₂) / ||u₂||² + (x · u₃) / ||u₃||².

To find x₂, we project x onto the subspace spanned by {u₄}. Since u₄ is a basis vector, the projection of x onto u₄ is simply the dot product of x with u₄ divided by the norm of u₄ squared. Hence:

x₂ = (x · u₄) / ||u₄||².

Thus, the vector x can be written as the sum of the two vectors: x = x₁u₁ + x₂u₄. Substituting the given values for u₁, u₂, u₃, and u₄, and evaluating the dot products and norms, we can find the components x₁ and x₂, and express x as the desired sum.

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Answer:

x<-1 so open circle going to the left

It will take approximately 11.9 years to triple the amount of the initial investment at an annual percentage rate of 6% compounded annually. This is calculated using the compound interest formula.

To calculate the duration required for your money to triple at an annual percentage rate of 6% compounded annually, you can use the formula for compound interest given as;

A = P(1 + r/n)^(nt),

Where; P is the principal amount, R is the annual interest rate, N is the number of times the interest is compounded per year, T is the time in years.

For this question,P = $1 (since we don't know the amount)

R = 6% = 0.06N = 1 (since the interest is compounded annually)

We want to know the time required (T) to get triple the amount of the initial amount.

This means that;

A = 3P

Therefore,

3P = P(1 + r/n)^(nt)

Dividing both sides of the equation by P,

3 = (1 + r/n)^(nt)

Since we want to calculate for time (T), we can use logarithms to solve.

Therefore, taking the natural logarithm of both sides of the equation,

ln(3) = ln(1 + r/n)^(nt)

Applying logarithmic laws,

ln(3) = nt ln(1 + r/n)

Solving for time (T),

T = ln(3)/(n ln(1 + r/n))

Substituting the values we have, we get;

T = ln(3)/(1 ln(1 + 0.06/1)) = ln(3)/ln(1.06) ≈ 11.9 years

It will take approximately 11.9 years to triple the amount of the initial investment at an annual percentage rate of 6% compounded annually. This is calculated using the compound interest formula.

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The man in a lighthouse tower 30 ft. high spots a ship at sea. The angle of depression from the man to the ship is 10°. How far is the ship from the base of the lighthouse?The problem involves an angle of depression, which is defined as the angle formed by a horizontal line and the line of sight that is directed downwards to an object.

A lighthouse tower is 30 feet tall. The line of sight from the man in the lighthouse to the ship forms an angle of depression of 10°.We can use trigonometry to solve for the distance between the lighthouse and the ship. We need to find the length of the side adjacent to the angle of depression. The distance we are looking for is the length of this adjacent side. So, we can use the tangent function to solve for the distance from the base of the lighthouse to the ship. The formula for tangent is tangent = opposite/adjacent. We know that the angle of depression is 10° and the opposite side is 30. The adjacent side is the distance we are trying to solve for.

tan θ = opposite/adjacent.  tan 10° = 30/adjacent0.1763 = 30/adjacent Adjacent = 30/0.1763Adjacent = 170.23 feet.

In this problem, we are given the height of the lighthouse, the angle of depression, and we are asked to find the distance between the ship and the base of the lighthouse. The first step is to draw a diagram of the situation. We can see that the line of sight from the man in the lighthouse to the ship forms an angle of depression of 10°.We know that the height of the lighthouse is 30 feet. We want to find the length of the side adjacent to the angle of depression, which is the distance we are looking for. To solve for this, we can use the tangent function.

The formula for tangent is tangent = opposite/adjacent. tan θ = opposite/adjacent tan 10° = 30/adjacent. We can cross-multiply and simplify the equation to solve for adjacent. adjacent = 30/tan 10°We can use a calculator to evaluate the tangent of 10°.tan 10° = 0.1763adjacent = 30/0.1763Adjacent = 170.23 feet .The ship is approximately 170.23 feet from the base of the lighthouse.

Therefore, we can conclude that the ship is approximately 170.23 feet from the base of the lighthouse.

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Answer:

1

Step-by-step explanation: