You put $4500 into an account earning 6% interest compounded annually.


Write an equation to model the situation

Answer: 54°

Step-by-step explanation:

We can see that this triangle is a right triangle (look at the little square in the triangle's corner-- that tells us that it's a right angle). A right angle is 90°

A triangle always has 180° in total.

So, we can add 90° and 36° and subtract the sum from 180°

180° - (90° + 36°) = 180° - 126° = 54°

Answer:

x = 54

Step-by-step explanation:

One of the properties for any triangle is that the sum of angles in the triangle will always equal 180 degrees. As one can see, one of the angles is (90) degrees, this is indicated by the box around the angle. It is given that one of the other angles is (36) degrees. One can call the unknown angle (x) and form an equation. Substitute in the given values and solve for (x).

(90) + (36) + (x) = 180

Simplify,

126 + x = 180

Inverse operations,

126 + x = 180

-126       -126

x = 54

Answer: yea

Step-by-step explanation:

The true statement is "Every seventh-grade class has 12 more students than a kindergarten class." (option d).

For the seventh-grade class, the mean is 32, which is larger than the mean for the kindergarten class. This means that, on average, seventh-grade classes have more students than kindergarten classes. The MAD for the seventh-grade class is 2, which is larger than the MAD for the kindergarten class.

This suggests that the deviation from the mean for each data point in the seventh-grade class is larger, on average 2 students, than for the kindergarten class. This means that the size of seventh-grade classes is more variable than kindergarten classes.

Option D is correct because while the difference between the means of the two classes is 12, this does not mean that every seventh-grade class has 12 more students than every kindergarten class.

Hence the c correct choice is option (d).

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Answer:

boys + girls =  45  -------(1)

There boys 17 more than girls, boys = girls + 17  ----------(2)

substitute (2) in (1)

girls + 17 + girls = 45

2 x girls + 17 = 45

2 x  girls = 45 - 17

2 x girls = 28

girls = 14

substitute in (2): boys = girls + 17 = 14 + 17 = 31

option D

Answer:

The answer is D

Step-by-step explanation:

Answer:

Option C,

y² = 18x, since the graph opens right

Answered by GAUTHMATH

The answer of the equation 8(x-3) +7=2x(4-17) is x=1/2.

An equation is a statement that says that the value of two mathematical expressions is equal i.e., it is a mathematical sentence that has two equal sides separated by an equal sign.

We have the equation : 8(x-3) +7=2x(4-17)

Here we are not given Lin's solution so we can not find the error in her solution but we will solve this equation and find the value of x.

            8(x-3) +7= 2x (4-17)    

      ⇒  8x - 24 +7 = 2x(-13)

      ⇒  8x -17= -26x

      ⇒  34x = 17

      ⇒  x= 17/34

      ⇒ x =1/2.

The solution of the above equation is x= 1/2.

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Answer:

 525 miles

Step-by-step explanation:

Two unit rates are given in this problem:

miles per gallon

gallons per mile

Since we want to find miles, the appropriate rate to use is miles per gallon:

\(distance = \frac{miles}{gallon} (gallons)\\distance = \frac{35 miles}{gallon} (15 gallons) = 525\)

Answer: 30 minutes

Step-by-step explanation:

1/10 miles = 1 minute

3 miles = x

1/10x = 3

Multiply both sides by 10

x = 30

Isa would run 3 miles in 30 minutes.

Hope this helped!

Answer: u = 7

Step-by-step explanation: because it is the exact same as the other side. and the other side is 7

Answer:

u = 7 Km

Step-by-step explanation:

the perimeter is the sum of the 3 sides.

given perimeter = 16 Km , then

u + 2 + 7 = 16

u +9 = 16 ( subtract 9 from both sides )

u = 7 Km

To be sure that at least three of the cards have the same face value, you would need to pick 3 cards. This is because the lowest number of cards with the same face value that can be achieved is 3, so if you pick 3 cards, you will guarantee that at least 3 of them have the same face value.

To be sure that at least four of the cards are diamonds, you would need to pick 5 cards. This is because the other 3 suits (clubs, hearts and spades) each have 13 cards, so if you pick 5 cards, you would have at least 4 cards of one suit (diamonds). To be sure that at least three of the cards have the same face value, you would need to pick 3 cards. This is because the lowest number of cards with the same face value that can be achieved is 3, so if you pick 3 cards, you will guarantee that at least 3 of them have the same face value.

At least four of them are diamonds: 5 cards

At least three of them are have the same face value: 3 cards

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Answer:

32

56

24

Step-by-step explanation:

Here is the full question :

Arthur is organising his collection of DVDs He has 112 altogether. The ratio of comedy films to action to horror is 4 : 7 : 3

How many of each type of DVD does he have?

the number of each dvd arthur has = ratio / sum of ratios) x total number of DVDs

Sum of ratios = 4 + 7 + 3 = 14

Comedy films = (4/14) x 112 = 32

Action = (7/14) x 112 = 56

Horror = (3/14) x 112 = 24

(a) The statement assumes that the population mean of radon in New Brunswick houses (β) is equal to the EPA cutoff of 4.

The null hypothesis can be written as:

H0: β = 4

(b) The alternative hypothesis can be written as:

Ha: β ≠ 4

This statement suggests that the population mean of radon in New Brunswick houses (β) is not equal to the EPA cutoff of 4.

(c) When testing this null hypothesis, a two-tailed test is used. This is because the alternative hypothesis does not specify a direction (greater than or less than), but instead allows for the possibility that the population mean can differ from the EPA cutoff in either direction.

(d) To test the null hypothesis, we need to use an estimator of β. In this case, the sample mean (x) will serve as the estimator of β. The formula for the variance of this estimator, assuming simple random sampling, is:

Var(x) = σ²/n

Here, σ represents the population standard deviation and n is the sample size. To estimate this variance formula, we need the sample standard deviation (s). The estimated variance formula becomes:

Var(x)≈ s²/n

To obtain a standard error for the estimator of β, we take the square root of the estimated variance:

SE(x) ≈ √(s²/n)

4. To test the null hypothesis using a t-test, we will compute the t-statistic using the formula:

t = (x-β) / (SE(x))

In this case, since β is known (4), the formula simplifies to:

t = (x- 4) / (SE(x))

To carry out the test at the 5% significance level (α = 0.05), we will compare the computed t-statistic to the critical value(s) from the t-distribution with appropriate degrees of freedom. The rejection rule is as follows: If the absolute value of the computed t-statistic is greater than the critical value(s), we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

The result of the test will indicate whether there is sufficient evidence to reject the null hypothesis or not.

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To find the largest four-digit value of t such that the expression is an integer, we need to set up an equation and solve for t.

Let's denote the given expression as x:

x = √(t - √(t - √(t - √(t - ...)))

To simplify the expression, we notice that the inner square root can be represented by x itself. So we can rewrite the equation as:

x = √(t - x)

Squaring both sides to eliminate the square root:

x^2 = t - x

Rearranging the equation:

x^2 + x - t = 0

To find the largest four-digit value of t, we can iterate through the values of t starting from 9999 and solve the quadratic equation for x. We are looking for a positive integer solution for x. Once we find the largest value of t that satisfies this condition, we have our answer.

By solving the quadratic equation for different values of t, the largest four-digit value of t that satisfies the condition is 9985.

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A $470 loan was taken out with a 4% simple annual interest rate for 5 years. Interest owed at the end of the loan is $94 ($470 x 0.04 x 5) in total, with the interest being calculated using the formula I = P x r x t. I represents the interest, P represents the principal, r represents the interest rate, and t represents the time in years.

Simple interest is the same throughout the loan period. It is the calculated interest based on the amount borrowed, the interest rate, and the length of time. In this problem, the loan amount is $470, the annual interest rate is 4%, and the loan term is 5 years.
To compute the interest owed at the end of the loan, use the simple interest formula:
I = P x r x t
Where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substitute the given values:
I = $470 x 0.04 x 5
I = $94
Therefore, the interest owed at the end of the loan is $94. The total amount to be paid back, which includes the principal and the interest, is $564 ($470 + $94).

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Answer:

y- intercept = 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - \(\frac{4}{3}\) , then

y = - \(\frac{4}{3}\) x + c

To find c substitute (- 3, 7 ) into the equation

7 = - \(\frac{4}{3}\) (- 3) + c

7 = 4 + c ⇒ c = 7 - 4 = 3 ← y- intercept

Answer:

48 iches

Step-by-step explanation:

720/15 = 48

Answer:

48:720

Step-by-step explanation:

Answer:

list 3

Step-by-step explanation:

if you look at list 3 "4.5 feet, 4.25 feet, 4 feet, 3.99 feet, 3.5 feet" you can easily see that it is going from greatest to smallest because 4.5 is larger than 4.25 and 4.25 is larger than 4 and 4 is larger that 3.99 by 0.01 as you see its only 0.01 diffrence but it is still larger

Answer:

List 3

Step-by-step explanation:

I got it right (;

If we express  \(3x^2-6x-2\) in the form  \(a(x-h)^2+k\), then a + h + k = -1

The given quadratic expression is:

\(3x^2-6x-2\)

To express \(3x^2-6x-2\) in the form \(a(x-h)^2+k\), follow the steps below

Rewrite \(3x^2-6x-2\) as  \(3x^2-6x+3-5\)

Factorize common terms

\(3(x^2-2x+1)-5\)

This can be further simplified as:

\(3(x-1)^2-5\)

Therefore, the vertex form of the equation  \(3x^2-6x-2\) is \(3(x-1)^2-5\)

Compare \(3(x-1)^2-5\) with  \(a(x-h)^2+k\)

a = 3, h = 1, k = -5

a  +  h  +  k  =  3  +  1 - 5

a  +  h  +  k  =  -1

Therefore if we express  \(3x^2-6x-2\) in the form  \(a(x-h)^2+k\), then a + h + k = -1

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Answer:

7:1

Step-by-step explanation:

There are two cubes, one with 14 cm and one with 2 cm. 14:2 is equal to 7:1.

The functions 1/x, 1-x², and 1-3x are linearly independent on any interval that does not contain x=0, but they are dependent at x=0.

To determine whether the functions 1/x, 1-x², and 1-3x are linearly independent, we can use the Wronskian method. The Wronskian of a set of functions f1(x), f2(x), ..., fn(x) is defined as:

W(f1, f2, ..., fn) = det | f1 f2 ... fn |

| f1' f2' ... fn' |

where f1', f2', ..., fn' are the derivatives of the functions with respect to x.

If the Wronskian is nonzero for all values of x in a given interval, then the functions are linearly independent on that interval. If the Wronskian is zero for at least one value of x in the interval, then the functions are linearly dependent on that interval.

For the functions 1/x, 1-x², and 1-3x, we have:

W(1/x, 1-x², 1-3x) = det | 1/x 1-x² 1-3x |

| -1/x² -2x -3 |

| 0 -2x 0 |

Expanding the determinant, we get:

W(1/x, 1-x², 1-3x) = -6/\(x^3\)

Since the Wronskian is nonzero for all values of x except x = 0, the functions 1/x, 1-x², and 1-3x are linearly independent on any interval that does not contain x = 0.

Therefore, the functions are linearly independent except at x = 0.

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The length of the curve r(t) over the interval 0 ≤ t ≤ 2π is approximately 285.97 units.

The length of the curve given by the vector-valued function r(t) over the interval [a, b] is given by the formula:

L = ∫[a,b] ||r'(t)|| dt

where r'(t) is the derivative of r(t) with respect to t and ||r'(t)|| is its magnitude.

In this case, we have:

r(t) = ⟨4cos(5t), 4sin(5t), t^(3/2)⟩

r'(t) = ⟨-20sin(5t), 20cos(5t), (3/2)t^(1/2)⟩

||r'(t)|| = √( (-20sin(5t))^2 + (20cos(5t))^2 + ((3/2)t^(1/2))^2 )

||r'(t)|| = √( 400sin^2(5t) + 400cos^2(5t) + (9/4)t )

||r'(t)|| = √( 400 + (9/4)t )

So the length of the curve over the interval [0, 2π] is:

L = ∫[0,2π] √( 400 + (9/4)t ) dt

Making the substitution u = 20t^(1/2)/3, we get:

du/dt = 10t^(-1/2)/3

dt = (3/10)u^(-1/2) du

When t = 0, u = 0, and when t = 2π, u = 20√(π)/3. Substituting these values and simplifying, we get:

L = ∫[0,20√(π)/3] √( 1 + u^2 ) du

Using the substitution x = sinh(u), we get:

dx/dt = cosh(u)

dt = dx/cosh(u)

When u = 0, x = 0, and when u = 20√(π)/3, x = sinh(20√(π)/3). Substituting these values and simplifying, we get:

L = ∫[0,sinh(20√(π)/3)] √( 1 + sinh^2(x) ) dx

L = ∫[0,sinh(20√(π)/3)] cosh(x) dx

Using the formula for the integral of cosh(x), we get:

L = sinh(sinh(20√(π)/3)) - sinh(0)

L ≈ 285.97

Therefore, the length of the curve r(t) over the interval 0 ≤ t ≤ 2π is approximately 285.97 units.

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I HOPE IT HELPED

Answer:

B. plant from variety Always grow taller than plant from variety B

The total amount including the tax rate is found as $34.

For the stated conditions in the question.

The original amount = $31.69.

The tax rate is 6%.

The total mount will be the sum of original amount and tax price.

First calculated the tax price;

6% of 31.69 = 6×31.69/100

6% of 31.69 = 1.9014

Tax price = $1.9014.

Total price = original amount + tax price

Total price = $31.69 + 1.9014

Total price = 33.5914

Total price = $34 (Round to the nearest cent.)

Thus, the total amount is estimated as $34.

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The image of ΔHOP with coordinates H(2,1), O(-3,4), and P(5,7).

(a) after 90° clockwise rotation is H'(1,-2,),O'(4,3),P'(7,-5) ,

(b) after 90° counterclockwise rotation is H''(-1,2),O''(-4,-3),P''(-7,5) ,

(c) after 180° rotation is H'''(-2,-1),O'''(3,-4),P'''(-5,-7) .

When a point (x,y) is rotated 90° in clockwise about the origin then the image after rotation becomes (y,-x) .

When a point (x,y) is rotated 90° in counterclockwise about the origin then the image after rotation becomes (-y,x) .

When a point (x,y) is rotated 180° about the origin then the image after rotation becomes (-x,-y) .

Part(a)

The ΔHOP with coordinates H(2, 1), O(-3, 4), and P(5, 7) is rotated 90° in clockwise direction ,

we know the points (x,y) becomes (y,-x),

So the image of ΔHOP after rotation becomes H' , O' , P'   .

H(2, 1) → H'(1,-2)

O(-3, 4) → O'(4,3)

P(5,7) →  P'(7,-5)

Part(b)

The ΔHOP with coordinates H(2, 1), O(-3, 4), and P(5, 7) is rotated 90° in counterclockwise direction ,

we know the points (x,y) becomes (-y,x),

So the image of ΔHOP after rotation becomes H'' , O'' , P''   .

H(2, 1) → H''(-1,2)

O(-3, 4) → O''(-4,-3)

P(5,7) →  P''(-7,5)

Part(c)

The ΔHOP with coordinates H(2, 1), O(-3, 4), and P(5, 7) is rotated 180°,

we know the points (x,y) becomes (-x,-y),

So the image of ΔHOP after rotation becomes H''' , O''' , P'''   .

H(2, 1) → H'''(-2,-1)

O(-3, 4) → O'''(3,-4)

P(5,7) →  P'''(-5,-7)

Therefore , The image of ΔHOP

(a) after 90° clockwise rotation is H'(1,-2,),O'(4,3),P'(7,-5) ,

(b) after 90° counterclockwise rotation is H''(-1,2),O''(-4,-3),P''(-7,5) ,

(c) after 180° rotation is H'''(-2,-1),O'''(3,-4),P'''(-5,-7) .

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Answer:

D

Step-by-step explanation:

the picture

The correlation coefficient of 0.88 reveals that there is an intense linear connection between the two variables.

It should be noted that to ascertain the correlation coefficient, we can utilize the formula:

r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

Retaining the same numeric values from before, we can compute:

r = (9(976) - (36)(605)) / sqrt[(9(182) - (36)^2)(9(11681) - (605)^2)] ≈ 0.88

Therefore, the correlation coefficient is fairly close to 0.88.

The correlation coefficient implies a strong positive relationship between hours expended studying and test outcomes. As the quantity of hours committed to studying increases, the test scores will tend to keep up accordingly. A correlation coefficient of 0.88 reveals that there is an intense linear connection between the two variables, and the line of best fit serves as a desirable standard representation of the data.

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Answer:

Step-by-step explanation:

It appears there is an error in the table. The correct table is:

\(\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-11}\vphantom{\dfrac12}\textsf{Hours spent studying $(x)$}&0&1&2&4&4&4&6&6&7&8\\\cline{1-11}\vphantom{\dfrac12}\textsf{Test score $(y)$}&35&40&46&65&67&70&82&88&82&95\\\cline{1-11}\end{array}\)

The simplest method to find the linear regression equation and the correlation coefficient for this data set is to use a statistical calculator.

After entering the data into a statistical calculator we get:

The regression line of y on x is y = a + bx.

Therefore, substitute the found values of a and b into the formula to write the linear regression equation for the given data set:

\(\boxed{y=34.27+7.79x}\)

The correlation coefficient is the value of r, so r = 0.98 to the nearest hundredth.

The correlation coefficient, r, measures the strength of the linear correlation between two variables. |t is always between +1 and -1.

As r = 0.98, there is a very strong positive correlation.

In context, this suggests that the more hours of studying for a test a student does, the higher their test score.

Answer:

-2,-9

Step-by-step explanation:

im not 100 perent sure ifthis is right or not

Answer:(-2,-9)

Step-by-step explanation: