Erica starts the year with
$
200
in her savings account. She deposits another
$
75
into it every month. Darrell starts the year with
$
350
in his savings account. He deposits another
$
50
into it every month.

Answer:

1089

Step-by-step explanation:

The original number is A0CD, We have that DC0A = 9 x A0CD.

If A =1, then D = 9 and we have:

9C01 = 9 x 10C9

In order for this expression to be true, the following must also be true:

(C x 9) + 8 must be divisible by 10, which means that C x 9 must end in a 2.

The only multiple of 9 (from 9 to 81) that ends in a 2 is 72.

72 = 9 x 8.

Therefore, C must be 8 and the original number is 1089. Multiply it by 9 to check the answer:

1089 x 9 = 9,081

Therefore, 1089 is correct.

The mean of this sample of car prices can be calculated by adding all the prices and dividing by the total number of dealers:

($35,700 x 2) + ($35,900 x 1) + ($36,200 x 3) + ($37,400 x 2) + ($37,900 x 2) = $326,500

$326,500 / 10 dealers = $32,650 (mean price)

To calculate the standard deviation, we first need to find the variance:

1. Subtract the mean from each individual price:

($35,700 - $32,650) = $3,050
($35,700 - $32,650) = $3,050
($35,900 - $32,650) = $3,250
($36,200 - $32,650) = $3,550
($36,200 - $32,650) = $3,550
($36,200 - $32,650) = $3,550
($37,400 - $32,650) = $4,750
($37,400 - $32,650) = $4,750
($37,900 - $32,650) = $5,250
($37,900 - $32,650) = $5,250

2. Square each of these differences:

$3,050^2 = $9,302,500
$3,050^2 = $9,302,500
$3,250^2 = $10,562,500
$3,550^2 = $12,602,500
$3,550^2 = $12,602,500
$3,550^2 = $12,602,500
$4,750^2 = $22,562,500
$4,750^2 = $22,562,500
$5,250^2 = $27,562,500
$5,250^2 = $27,562,500

3. Add up all of these squared differences:

$9,302,500 + $9,302,500 + $10,562,500 + $12,602,500 + $12,602,500 + $12,602,500 + $22,562,500 + $22,562,500 + $27,562,500 + $27,562,500 = $167,052,500

4. Divide the total by the number of dealers minus 1 (this is called the sample variance):

$167,052,500 / 9 = $18,561,388.89

5. Take the square root of the sample variance to get the standard deviation:

√$18,561,388.89 = $4,307.17 (standard deviation)

So the mean price of this sample of car prices is $32,650 and the standard deviation is $4,307.17.

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Given

The data is given

10,13,14,15,17,18,20,30,35

Answer:

130,110,40,90,165

Step-by-step explanation:

supplementary angles add up to 180

so 180-50= 130

180-70=110

etc

Answer:

(0,1/3)

Step-by-step explanation:

always remember, the y-intercept is when x=0 because its on the y-axis.

so, the y-intercept would always just be the constant :1/3.

Answer:

(0, 1/3)

y-int is 1/3

Step-by-step explanation:

Answer:

I think it is $91.89.

Step-by-step explanation:

1. Take the number and add sales tax by multiplying 0.0725 ( since that is what the percentage is in a decimal form). Then add that to the original and you have what it would be plus sales tax: $60.05.

2. Then you would need to multiply by 0.18. You would get 10.809

3. Next, subtract the 10.809 from $60.05 and the answer is $49.24.

I hope this helps! :)

Answer:

x = 27

Step-by-step explanation:

The little square at the bottom of the figure means that that angle is a right angle, or 90°. Knowing that it's a 90° angle and that one section of the adjacent angle is 63°, we just calculate 90-63 to get 27, the value of x.

(a)i. Evaluating the constant:

\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)

Therefore, the probability density function is:

\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:

From the graph, it is observed that the density function is skewed to the left.

(b)i. The mean:

\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)

ii. The second moment about the origin:

\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)

Therefore, the variance is:

\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)

iii. The standard deviation:

$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)

i. The cumulative distribution function:

\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)

ii. The probability density function can be obtained by differentiating the cumulative distribution function:

\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)

iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)

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The exponential function has the following form:

The function goes through the points ( 0, 19) and ( 2, 171 )

We will use the points to find the values of a and b

Substitute with the point ( 2, 171 ) and the value of a to find b

So, the answer will be:

(a) The area of the rectangle with sides 3 cm and 4 cm is 12 square centimeters.

(b) The area of the rectangle with sides 12 m and 21 m is 252 square meters.

(a) Rectangle with sides 3 cm and 4 cm:

To find the area of a rectangle, we multiply the length of one side, called the base, by the length of an adjacent side, called the height. In this case, the length of one side is 3 cm, and the length of the adjacent side is 4 cm.

Area of the rectangle = length × width

= 3 cm × 4 cm

= 12 cm²

(b) Rectangle with sides 12 m and 21 m:

Using the same formula for calculating the area of a rectangle, we can find the area of a rectangle with sides 12 m and 21 m.

Area of the rectangle = length × width

= 12 m × 21 m

= 252 m²

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Complete Question:

Find the areas of the rectangles whose sides are:

(a) 3 cm and 4 cm

(b) 12 m and 21 m

Answer:

45 mph

Step-by-step explanation:

It took the car 4 hours to travel 180 miles

Then

It took the car 4/4 hours to travel 180/4 miles

Since 4/4 = 1 and 180/4 = 45

Then

It took the car 1 hours to travel 45 miles

Therefore ,the car was it going at 45 mph

The mean of the given fuel prices data set is $4.61 with a standard deviation of $1.62.

To calculate the mean and standard deviation in Excel, you can use the following functions:

Mean: The AVERAGE function calculates the mean of a range of values. In this case, enter "=AVERAGE(A1:A30)" in an Excel cell, assuming the data is in cells A1 to A30.

Standard Deviation: The STDEV.S function calculates the standard deviation of a range of values. Enter "=STDEV.S(A1:A30)" in an Excel cell to calculate the standard deviation of the data set.

Using the mean ($4.61) and standard deviation ($1.62), we can now proceed to calculate the Confidence Interval.

The Confidence Interval can be determined using the formula: E = Z * (σ / √n)

In the formula, Z is the z-score corresponding to the desired level of confidence (e.g., 95% confidence corresponds to a z-score of approximately 1.96), σ is the population standard deviation (which can be estimated using the sample standard deviation in this case), and n is the sample size.

Let's assume we want a 95% confidence interval for the data set with a sample size of 30. We can use the formula "=CONFIDENCE.NORM(0.05, STDEV, 30)" in an Excel cell to calculate the E value.

Substituting the values into the formula, we get E = 1.96 * (1.62 / √30) ≈ 0.595.

Now, we can set up the confidence interval using the mean and E value:

Confidence Interval = (mean - E, mean + E)

Confidence Interval = ($4.61 - $0.595, $4.61 + $0.595)

Confidence Interval = ($4.015, $5.205)

Therefore, the 95% Confidence Interval for the given fuel prices data set is approximately $4.015 to $5.205.

In summary, the mean of the fuel prices data set is $4.61 with a standard deviation of $1.62. The 95% Confidence Interval for the data is approximately $4.015 to $5.205.

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Answer:

(17, -13) (17, 8) --> In this problem, we use the y2-y1 over x2 - x1 formula.

Step-by-step explanation:

Step 1: Plug In--> 8-(-13)

                            17 - 17

Step 2: Simplify: 21

                             0

Answer: Undefined. Vertical line on graph.

Answer: 21

Step-by-step explanation: The first thing you should have noticed is that x is the same for both coordinates; in other words, x=17, which means there's no change and x, and it will therefore be a straight vertical line. From there, you can find the change in y to determine the slope (because slope is rise over run). Since 8-(-13)=21, the slope is 21.

Investment X earns the greater amount of interest over a period of 2 years.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let's consider that Ian invests in X, then:

Principle amount, P = $6,000
Time, T = 2 Years

Rate of Interest, R = 4.5% at simple Interest = 0.045

The interest earned is:

Interest = PRT = $6,000 × 0.045 × 2 = $540

Now, consider that Ian invests in Y, then:

Principle amount, P = $6,000
Time, n = 2 Years

Rate of Interest, R = 4% at Compound Interest = 0.04

The interest earned is:

Interest = P(1+R)ⁿ - P

            = $6,000(1+0.04)² - $6,000

            = $489.6

Since $540>$489.6, therefore, Investment X earns the greater amount of interest over a period of 2 years.

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Answer:35°

Step-by-step explanation:55+90=145   180-145=35

Answer:

a = 35

Step-by-step explanation:

Straight angle theorem state that a straight line has an angle of 180 degrees

a + 90(right angle) + 55 = 180

a = 35

The directional derivative of a function f(x, y) at a point (a, b) in the direction of a unit vector u = ⟨cosθ, sinθ⟩ is given by the dot product of the gradient of f at (a, b) and the unit vector u.

That is, D_uf(a, b) = ∇f(a, b) · u

Here, f(x, y) = xy^3 - x^2, so ∇f(x, y)

= ⟨y^3 - 2x, 3xy^2⟩.

At the point (1, 4), we have ∇f(1, 4) = ⟨60, 192⟩.

The direction indicated by the angle theta = π/3 is u = ⟨cos(π/3), sin(π/3)⟩ = ⟨1/2, √3/2⟩.

Therefore, the directional derivative of f at (1, 4) in the direction of u is:

D_uf(1, 4) = ∇f(1, 4) · u

= ⟨60, 192⟩ · ⟨1/2, √3/2⟩

= 60/2 + 192(√3/2)

= 30 + 96√3

So the directional derivative of f at (1, 4) in the direction of θ = π/3 is 30 + 96√3.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

kabul is yhe capital city

kabul is the capital city of Afghanistan.

Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

▪︎▪︎▪︎▪︎▪︎▪︎

Answer:

subtract 5 , m=(-15)

Step-by-step explanation:

15-5

=10

n:

5-10

=(-5)

m:

(-5)-10

=(-15)

hope it help

y  =  − 1 /8x - 19/4

i think

Answer:

You = bronze

Your brother = silver

Your sister = gold

Step-by-step explanation:

Your marks: 40/60

Your brother's marks: 46/60

Your sister's marks: 49/60

You can simplify the fractions, but you don't have to:

40/60 = 2/3

46/60 = 23/30

49/60 = 49/60

Now, divide each of the numerators by the denominators (turn the fraction into a decimal).

2/3 = 0.6667

23/30 = 0.7666667

49/60 = 0.8166667

(Note that these are all approximations as the real answers go on forever)

Lastly, multiply them all by 100 to get the percent.

0.6667 x 100 = 66.67% - bronze

0.76667 x 100 = 76.667% - silver

0.816667 x 100 = 81.6667% - gold

Answer:

x = 11

Step-by-step explanation:

Using Secants ad Segments Theorem we can say;

(x + 7) (7) = (15 + 6) (6)

7x + 49 = (21) (6)

7x + 49 = 126

7x = 77

x = 11

Hope this helps!

The radius of the oatmeal container is 0.2 inches.

The surface area of the plastic is 0.08π square inches

The base and lid are made of plastic and have a radius of R.

The base and lid have a combined surface area of:

πr² + πr² = 2πr² square inches

The total surface area of the oatmeal container is 40 square inches.

The surface area of the cardboard is 16πr square inches and the surface area of the plastic is 2πr² square inches.

Thus, we have the equation:

40 = 16πr + 2πr²

We can solve for R as follows:

16πr + 2πr² = 40

2πr^2 + 16πr - 40 = 0

2πr^2 + 20πr - 4πr - 40 = 0

20r(πr + 2) - 4(πr + 2) = 0

(20r - 4)(πr + 2) = 0

20r - 4 = 0 or πr + 2 = 0

20r = 4 or πr = -2

r = 0.2

Thus, the radius of the oatmeal container is 0.2 inches.

The surface area of the plastic is 2πr² = 2π(0.2)² = 0.08π square inches

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Answer:

first one is simnple cross multiply and divide

12*7=4x

84=4x

x=21

2nd same process but more steps

7x=5(x+8)

7x=5x+40

7x-5x=40

2x=40

x=20

Step-by-step explanation:

Iku is correct, because the function has no real zeros because there are no x-intercepts.

We have to given that;

Iku and Zachary are finding the number of real zeros of the function graphed at the right.

Here, By graph we see that;

The graph is not cut at x - axis.

Hence, There is no real solution.

So, Iku is correct, because the function has no real zeros because there are no x-intercepts.

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Answer:

(7x - 3)

Step-by-step explanation:

you can use synthetic division to divide 21x² - 44x + 15 by 3x-5

The solution is, 7x - 3 , is the length of the parking lot.  

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

given that,

The area of a rectangular parking lot is 21x^2 - 44x + 15.

The width of the parking lot is 3x - 5.

now, we have to find, the length of the parking lot.

we know that,

Area of a rectangle (A) is the product of its length (l) and width (w). Basically, the formula for area is equal to the product of length and breadth of the rectangle.

i.e. A = l * w

here,

A = 21x^2 - 44x + 15

w = 3x - 5

so, length = A/w

i.e. length = 21x^2 - 44x + 15 / 3x - 5

                 = 7x - 3

Hence, 7x - 3 , is the length of the parking lot.  

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The activation energy of the reaction is approximately 126.8 kJ/mol. The calculation was done using the Arrhenius equation and the natural logarithm of the rate constants at the two temperatures.

To calculate the activation energy of a reaction, we can use the Arrhenius equation:

k = A * e⁽⁻ᴱᵃ/ᴿᵀ⁾

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

We have two rate constants at different temperatures, so we can set up two equations:

k₁ = A * e⁽⁻ᴱᵃ/ᴿᵀ₁⁾

k₂ = A * e⁽⁻ᴱᵃ/ᴿᵀ₂⁾

We want to solve for Ea, so we can take the natural logarithm of both sides of each equation:

ln(k₁) = ln(A) - Ea/RT₁

ln(k₂) = ln(A) - Ea/RT₂

We can subtract the second equation from the first to eliminate ln(A):

ln(k₁) - ln(k₂) = Ea/R * (1/T₂ - 1/T₁)

Now we can solve for Ea:

Ea = -R * (ln(k₁) - ln(k₂)) / (1/T₂ - 1/T₁)

Plugging in the given values, we get:

Ea = -8.314 J/mol/K * (ln(6.20 x 10⁻⁴) - ln(2.39 x 10⁻²)) / (1/760 K - 1/700 K)

Ea ≈ 126.8 kJ/mol

Therefore, the activation energy of the reaction is approximately 126.8 kJ/mol.

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