0.9(x-20)=830
What does x equal?

Answer:

  7/9

Step-by-step explanation:

The slope of the line between two given points is found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (5 -(-2))/(3 -(-6)) = (5+2)/(3+6) = 7/9

The slope of the line is 7/9.

_____

Additional comment

The slope of a line is the same everywhere, so the slope of the segment from (x, y) to A is the same:

  (y -(-2))/(x -(-6)) = 7/9 . . . . use the slope equation

  9(y +2) = 7(x +6) . . . . . . . multiply by 9(x+6)

  9y +18 = 7x +42 . . . . . . eliminate parentheses

  7x -9y = -24 . . . . . . . subtract 9y+42

This is the standard form of the equation for the line through the two points. The slope-intercept form would be ...

  y = 7/9x +8/3

The length of side AB is 15 units.

Given that triangles ADE and ABC are similar, and the length of side AC is 12, the length of side AE is 8 and the length of side AD is 10.

We need to find out the length of side AB.Since triangles ADE and ABC are similar, the corresponding sides are proportional.

Therefore, we have the proportion:AD / AB = AE / AC

So, we can find the length of AB by rearranging the proportion:

AB = AD × AC / AE

Since triangles ADE and ABC are similar, we can use the similarity property to indicate that corresponding sides of similar triangles are proportional.

Let x be the length of side AB.

Knowing the ratio of the corresponding sides, we can establish the ratio:

AE / AB = DE / BC

Substitute the given values:

8 / x = 10 / 12

To solve for x can do cross multiplication.

Solve the resulting equation:

8 * 12 = 10 * x

96 = 10x

Divide both sides by 10:

96 / 10 = x

x = 9.6

Taking the given values:

AB = 10 × 12 / 8AB

= 15

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Adding integers with a common sign.

When adding two integers with a common sign, we just add the absolute value of the numbers and the resulting answer is marked with the same sign given in the question.

This question has two possible answers.

Possibility 1:

Both the integers are of positive sign. As a result, the resulting integer after addition is positive.

Example:

Let c = 45 and d = 53.

The sum of c and d is then

sum = c + d = 45 + 53 = 98

Possibility 2:

Both the integers are of negative sign. As a result, the resulting integer after addition is negative.

Example:

Assume c = -23 and d = -61.

The sum of c and d is then

sum = c + d = (-23) + (-61) = -(23 + 61) = -84

Hence, we have added integers with a common sign.

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As the actual probability is greater than 68%. The statement "p(z < 1) < 68%" is false.

According to the empirical rule (also known as the 68-95-99.7 rule), approximately 68% of the observations in a standard normal distribution fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.

Since the statement is asking for the probability that the random variable z is less than 1, we need to find the area under the standard normal curve to the left of 1.

This represents the probability of z being less than 1.

Using the empirical rule, we know that within one standard deviation of the mean, which is 0 for the standard normal distribution, approximately 68% of the data lies.

Therefore, the probability P(z < 1) is less than 68%.

To find the precise probability, we can use a standard normal distribution table or a statistical software.

Consulting the table or using software, we can determine that P(z < 1) is approximately 0.8413 or 84.13%.

Therefore, the statement "p(z < 1) < 68%" is false. The actual probability is greater than 68%.

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The value of 6½ - 1⅓ is 5 ⅙

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

To solve 6½ - 1⅓ ;

we make the mixed fraction improper fraction

= 13/2 - 4/3

= (39-8)/6

= 31/6

= 5 1/6

therefore The value of 6½ - 1⅓ = 5 1/6

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Step-by-step explanation:

\(6 \frac{1}{2} - 1\frac{1}{3} = 5 \frac{1}{6} \)

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Answer:

x=30°

y=15°

z=150°

Step-by-step explanation:

2x+90+x=180°

2x=180°-90°

x=90/3

x=30

2y=x

y= 30/2

y=15°

2y°+z°=180°

2(15°)+z°=180°

z=180°-30°

z=150°

Hope it helps! :)

The total money spent on passes and lunch for each student was $8.63.

Total money spent on passed = 651.21

Total number of people on field trip = 46 + 3

Performing addition

Total number of people on field trip = 49

Money spent on each pass = 651.21/49

Performing division

Money spent on each pass = $13.29

Total money spent on students = 396.98

Total number of students = 46

Money spent on lunch for each student = 396.98/46

Performing division

Money spent on lunch for each student = $8.63

Total money spent on each person for pass and lunch is $8.63.

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The hypothesis test statement below is a Type I Error Failing to reject the claim that community college students pay at least $1,250 per year on textbooks when the actual amount that community college students pay for textbooks is actually less than $1,250 per year. Option C is the correct answer.

A Type I Error occurs when the null hypothesis is wrongly rejected, leading to the conclusion that there is a significant effect or difference when, in reality, there is no such effect or difference.

In this case, option c represents a Type I Error because it falsely fails to reject the claim of paying at least $1,250 per year on textbooks when the actual amount is less than $1,250.

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The ratio of the number of unshaded to shaded squares is 7 : 3.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

It is also defined as the fraction of one quantity with respect to other.

The ratio of a and b is denoted as a : b.

Given is a grid of squares which is given below.

Total number of squares = 10

Of that,

Number of shaded squares = 3

Number of unshaded squares = 7

We have to find the ratio of unshaded to shaded squares in the grid which is 7 / 3 or 7 : 3.

Ratio of unshaded squares to shaded squares = 7 : 3

Hence 7 : 3 is the ratio of unshaded to shaded.

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The correct answer is A. \(300ax^2(ax^3 - 1)^{99\). This result shows that the derivative of f(x) by chain rule  is equal to   \(300ax^2(ax^3 - 1)^{99\)

To find the derivative of the function \(f(x) = (ax^3 - 1)^{100\), we can apply the chain rule. Let's denote \(g(x) = ax^3 - 1\), and consider the function \(h(u) = u^{100\)

The derivative of h(u) with respect to u is \(h'(u) = 100u^{99.\)

Now, using the chain rule, the derivative of f(x) with respect to x is given by: \(f'(x) = h'(g(x)) * g'(x).\)

Applying this to our function, we have:

\(f'(x) = 100(ax^3 - 1)^{99 }* (3ax^2).\)

Simplifying further, we get:

\(f'(x) = 300ax^2(ax^3 - 1)^{99.\)

Therefore, the correct answer is A. \(300ax^2(ax^3 - 1)^{99\). This result shows that the derivative of f(x) by chain rule  is equal to   \(300ax^2(ax^3 - 1)^{99\).

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The standard deviation of a set of seventeen numbers described by Σx=272 Σx² = 11849​ is 21.

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

We have Σx=272 and Σx² = 11849​.

n= 17

So, the Variance of the Data

= Σx²/n - (Σx/ n)²

= 11849 / 17 - (272/17)²

= 697 - 256

= 441

Then, the Standard deviation is

= √Variance

= √441

= 21

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A symbol that could be written in both circles in order to represent this system algebraically include the following: C. <.

In Mathematics, there are several rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:

In this context, we can logically deduce that the most appropriate inequality symbol to represent the solution to the system of inequalities is the less than (<) because the dashed boundary lines are shaded below.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The straight-line distance from the wilderness area to the Morrisons' campsite is approximately 5 miles.

To find the straight-line distance from the wilderness area to the Morrisons' campsite, we can use the Pythagorean theorem.

Let's consider the campsite as the origin (0, 0) on a coordinate plane. The wilderness area is located 3 miles due north and 4 miles due east from the campsite. Therefore, its coordinates are (4, 3).

Using the Pythagorean theorem, the straight-line distance d is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates of the campsite (0, 0) and the wilderness area (4, 3) into the formula, we get:

d = √((4 - 0)² + (3 - 0)²)

= √(4² + 3²)

= √(16 + 9)

= √25

= 5

Therefore, the straight-line distance from the wilderness area to the Morrisons' campsite is approximately 5 miles.

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Using Cosine law,

the distance between pilot's current position and his starting position is 2596 miles.

Cosine law:

The law of cosines can help you find the side lengths of a triangle. The sum of the squares of the remaining side lengths minus the product of twice the remaining side length times the opposite cosine angle.

Let a, b, and c be the sides and A, B, and C

be the corners of the triangle.

By the Law of Cosines (also called the Cosine Rule) says:

c² = a²+ b² − 2ab cos(C)

We are given that the constant speed = 650mph

A pilot flies in a straight path for 1 h 45 min. Thus, time = 1.75 hours

The distance travelled in 1.75 hrs (a) = 1.75 × 650

= 1137.5 miles

The pilot makes a course correction, heading 15 degrees to the right of her original course, and flies 2 h in the new direction.

Angle = 15°

The distance traveled in 2 hrs and 30 minutes (b)

= 650×2.5 = 1625 miles

let the distance between pilot current position and starting position be c miles .

Determining the length of c by using the Cosine law: c² = a²+ b² − 2ab cos(C)

putting all the values into above equation

c² = (1137.5)² + (1625)² - 2×1625(1137.5)Cos (15)

=> c² = 6740459.38

=> c = 2596.23 ~ 2596 miles

Hence, the distance between pilot's current position and starting position is 2596 miles.

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Answer:

r=d/t

r=360 cm / 9 sec= 40 cm per second

Hope that helps :)

Answer:

40 centimeters per second.

Step-by-step explanation:

360 divided by 9= 40

ChIcKeN nUgGeTs :>

In July, despite traveling away from home, the individual's electricity consumption amounted to $19.24. However, their solar panel generated $22.75 worth of electricity. Therefore, their amount due for July would be -$3.51.

During July, the individual's electricity consumption was $19.24. This implies that their usage exceeded the electricity generated by their solar panel. The solar panel, on the other hand, generated $22.75 worth of electricity. To calculate the amount due, we need to subtract the generated electricity from the consumption.

$19.24 (electricity consumption) - $22.75 (electricity generated) = -$3.51

The negative sign indicates that the individual's solar panel generated more electricity than their actual consumption. In other words, they produced an excess of $3.51 worth of electricity. Consequently, they would not owe any payment for July but would have a credit of $3.51 that could be carried forward to subsequent months. This credit can help offset future electricity bills or be utilized in the form of a rebate, depending on the individual's agreement with their electricity provider.

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Answer:

equation 400-15x. 7 weeks

Step-by-step explanation:

400-15x

4 cubic centimeters.

Brainliest would be great. Comment below if it helped!

Answer:

The volume for this object is 4.

Step-by-step explanation:

For each block, we need to multiply using the volume formula which is

Length x Width x Height

So, if the side lengths for all these blocks are 1. That means we would do 1x1x1 for every block. Since there are 4 blocks that means our equation for the whole object would be 1+1+1+1 or simply 1x4. And we all know the answer to our equation 1 x 4 is 4.

, Hope this helps :)

Have a great day!!

Answer:

X= Y/200 - 3/2

Step-by-step explanation:

WITHOUT using a calculator, the value of: tan 2P​ is 1/6

We can find the value of angle PRQ as:

angle PRQ = (180 - 90 - 2PRQ) degrees

         = (180 - 90 - 2*0) degrees

         = 90 degrees

This means that triangle PQR is a 45-45-90 triangle,

where PR = PQ = 24 and QR = 10.

From the ratios of sides in a 45-45-90 triangle,

we know that:

tan P = 1

sin P = cos P = 1/√2

Let's consider triangle SQR. The value of sin SQR, which is 3/10. We can use the Pythagorean theorem to find the length of SQ:

\(SQ^2 = QS^2 + SR^2\)

\(SQ^2 = 8^2 + 6^2\)

\(SQ^2 = 100\)

SQ = 10

Now, we can find the length of QR by subtracting the length of SR from SQ:

QR = SQ - SR

QR = 10 - 6

QR = 4

Using the ratios of sides in a right-angled triangle, we can find the values of sin 2P and cos 2P:

sin 2P = QR/PR = 4/24 = 1/6

cos 2P = PQ/PR = 24/24 = 1

Finally, we can use the identity tan 2P = sin 2P / cos 2P to find the value of tan 2P:

tan 2P = sin 2P / cos 2P

      = (1/6) / 1

      = 1/6

Therefore, the value of tan 2P is 1/6.

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Answer:

10 and 11

Step-by-step explanation:

The square root of 104 is 10.1980390272. This falls between the whole numbers 10 and 11.

If the linear correlation between an independent (x) and dependent (y) variable is:  f. none of the above.

The basis for basic (bivariate) regression is the linear correlation between an independent variable (x) and a dependent variable (y). The degree and direction of the relationship between the variables are measured by this.

Although a causal relationship between the variables may exist, the linear correlation does not prove it. Correlation merely assesses how much the variables differ collectively.

Therefore the correct option is F.

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Answer:

the multiplication of rational numbers is distributive over addition of rational numbers.

As the interest rate increases from 10 percent to 11 percent, the present value of the bond decreases from $1,074.47 to $1,058.31. Conversely, when the interest rate decreases to 9 percent, the present value increases to $1,091.19. This is because the discount rate used to calculate the present value is inversely related to the interest rate, meaning that as the interest rate increases, the present value decreases, and vice versa.

To compute the present value of a five-year, 10 percent coupon bond with a face value of $1,000, we need to discount the future cash flows (coupon payments and face value) by the appropriate interest rate.

Step 1: Calculate the present value of each coupon payment.
Since the bond has a 10 percent coupon rate, it pays $100 (10% of $1,000) annually. To calculate the present value of each coupon payment, we need to discount it by the interest rate.

Using the formula: PV = C / (1+r)^n
Where PV is the present value,

C is the cash flow,

r is the interest rate, and

n is the number of periods.

At an interest rate of 10 percent, the present value of each coupon payment is:
PV1 = $100 / (1+0.10)^1 = $90.91

Step 2: Calculate the present value of the face value.
The face value of the bond is $1,000, which will be received at the end of the fifth year. We need to discount it to its present value using the interest rate.

At an interest rate of 10 percent, the present value of the face value is:
PV2 = $1,000 / (1+0.10)^5 = $620.92

Step 3: Calculate the total present value.
To find the present value of the bond, we need to sum up the present values of each coupon payment and the present value of the face value.
Total present value at an interest rate of 10 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,074.47

When the interest rate goes to 11 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 11 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,058.31

When the interest rate goes to 9 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 9 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,091.19

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The transfer function H(s) = (62,893)/(s + 62,893) can be transformed to a digital filter representation H(z) using the bilinear transform.

The bilinear transformation is a common method used for converting analog filters to digital filters. It maps the entire left-half of the s-plane (analog) onto the unit circle in the z-plane (digital). The transformation equation is given by:

s =\((2/T) * ((1 - z^(-1)) / (1 + z^(-1)))\)

where s is the Laplace variable, T is the sampling period, and z is the Z-transform variable.

To convert the given analog LPF transfer function H(s) = (62,893)/(s + 62,893) to a digital filter representation, we substitute s with the bilinear transformation equation and solve for H(z):

H(z) = H(s) |s = \((2/T) * ((1 - z^(-1)) / (1 + z^(-1)))\)

= \((62,893) / (((2/T) * ((1 - z^(-1)) / (1 + z^(-1)))) + 62,893)\)

Simplifying the equation further yields the digital filter transfer function H(z):

H(z) = \((62,893 * (1 - z^(-1))) / (62,893 + (2/T) * (1 + z^(-1)))\)

The resulting H(z) represents the digital filter equivalent of the given 1st order analog LPF. This transformation enables the implementation of the filter in a digital signal processing system.

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\(9 = -4x - 3\\9+3 = -4x\\-4x = 9 + 3\\-4x = 12\\x = \frac{12}{-4}\\ x = -3\)

Hope that helped!