What is the surface area of the regular pyramid below

Answer:

  y +2 = 2(x +3)

Step-by-step explanation:

The equation in point-slope form for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

The slope of your given line is the coefficient of x, -1/2. The slope of a perpendicular line will be the negative reciprocal of that: -1/(-1/2) = 2. So, you have m = 2, (h, k) = (-3, -2), and your desired equation is ...

  y -(-2) = 2(x -(-3)) . . . . . . which can be simplified to ...

  y +2 = 2(x +3)

Answer:

Step-by-step explanation:

The residual is the difference between the actual value and that predicted by the model.

1. actual - predicted = 5.2 - 4.8 = 0.4

__

2. actual - predicted = 20 - (4·3 +10) = 20 -22 = -2

Answer:

C. 55°

Step-by-step explanation:

Note the total measurement of angles for a triangle. The total measurement of all angles in a triangle = 180°

Note that m∠C is a right angle (as shown through the square), and that right angles = 90°

Subtract to find the measurement of the unknown angle (∠B)

∠B = 180 - (∠A + ∠C)

∠B = 180 - (35 + 90)

Simplify. Combine like terms. First, add (solve parenthesis), then subtract.

∠B = 180 - (125)

∠B = 55

m∠B = C. 55°

~

Answer:D

Step-by-step explanation:

125

Answer:

A'(-1,-3)

B'(-2,-2)

C'(-4,-3)

Step-by-step explanation:

The rotation by 90° counterclockwise about the origin has the rule

[tex](x,y)\rightarrow (-y,x)[/tex]

So, the vertices of the triangle ABC have the images:

[tex]A(-3,1)\rightarrow A'(-1,-3)\\ \\B(-2,2)\rightarrow B'(-2,-2)\\ \\C(-3,4)\rightarrow C'(-4,-3)[/tex]

see attached diagram for details.

Answer:

  cot(θ) = 5/6

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you the tangent relationship is ...

  Tan = Opposite/Adjacent

The cotangent function is the inverse of the tangent function, so ...

  Cot = Adjacent/Opposite

For your angle, the adjacent side of the triangle is the x coordinate, 5; the opposite side is the y coordinate; 6. Then the cotangent is ...

  cot(θ) = 5/6

Answer:

14%

Step-by-step explanation:

If the selected student is a male, that reduces the population to consider, to 14 (4 + 6 + 2 + 2).

How many male juniors?  2

So, the chance for the random student to be a junior if he's a male, are 2 out of 14.

P = 2/ 14 = 1/ 7 = 14.29%

Rounded to the nearest whole percent: 14%

Answer:

[tex]x =38.7\°[/tex]

Step-by-step explanation:

By definition, the tangent of a x-angle is defined as

[tex]tan(x) =\frac{opposite}{adjacent}[/tex]

For this case

[tex]opposite = 8[/tex]

[tex]adjacent = 10[/tex]

Therefore we have that

[tex]tan(x) =\frac{8}{10}[/tex]

[tex]x =arctan(\frac{8}{10})[/tex]

The answer is:

[tex]x =38.7\°[/tex]

Answer:

1728 in³

Step-by-step explanation:

A 12-inch cube has a volume of (12 in)³ = 12³ in³ = 1728 in³.

The box will hold 1728 cubic inches.

To determine the volume of the box, which is the amount of space it can hold, one must calculate the product of its length, width, and height. Since the box measures 12 inches on each side, it is a cube. The volume ( V ) of a cube is given by the formula:

[tex]\[ V = a^3 \][/tex]

where a is the length of one side of the cube. In this case,  a = 12 inches. Plugging this value into the formula, we get:

[tex]\[ V = 12^3 \] \[ V = 12 \times 12 \times 12 \] \[ V = 144 \times 12 \] \[ V = 1728 \][/tex]

Therefore, the volume of the box, or the number of cubic inches it will hold, is 1728 cubic inches.

Hello There!

The answer would be "I and III"

If Isabelle makes these changes, she will get charged an overdraft fee on 2 days. The days will be Thursday and Saturday.

Answer:

B

Step-by-step explanation:

Answer:

1/2 to land on heads

1/5 spinner

2/6=1/3 dice

10/16=5/3 marbles

32 out of 64

12/30

13 out of 39

125/200

Answer:

Two events are mutually exclusive if they can't both happen. Independent events are events where knowledge of the probability of one doesn't change the probability of the other. Two events are mutually exclusive when they cannot occur at the same time. For example, if we flip a coin it can only show a head OR a tail, not both. Independent event: The occurrence of one event does not affect the occurrence of the others.

Independent events do not affect each other's occurrence, while mutually exclusive events cannot occur at the same time. The concepts are distinct and significant in probability theory.

Independent vs Mutually Exclusive Events

Independent events and mutually exclusive events are not the same in probability theory. Two events are independent if the occurrence of one event does not affect the probability of the other event occurring. The mathematical representation of this is P(A AND B) = P(A)P(B). On the other hand, two events are mutually exclusive if they cannot occur at the same time, meaning the events do not share any outcomes and the probability of both events occurring together, P(A AND B), is zero.

An example of independent events might be rolling a dice and flipping a coin. Whether the dice shows a six does not affect whether the coin shows heads. An example of mutually exclusive events would be drawing a heart or a club from a deck of cards as a single card cannot be both a heart and a club.

Answer:

The surface area of the composite figure = 1172.08 inches²

Step-by-step explanation:

* Lets explain the figure

- There is a cylinder with diameter 8 inches and height 9 inches

- Rectangular prism with dimensions 16 , 11 , 11 inches

- The surface area of the cylinder will be the curved area and the

  top base

- The surface area of the prism will be the surface area of one base ,

 four side faces and top face which is the remaining from the subtraction

 of the rectangular base and the circular base

* Lets solve the problem

# The surface area of the cylinder

∵ The diameter of the base of the cylinder is 8 inches

∵ The diameter = twice the radius

∴ 8 = 2r ⇒ divide both sides by 2

∴ r = 4 inches

∵ The area of the circle = πr²

∴ The area of the base = π(4)² = 16π inches²

∵ π = 3.14

∴ The area of the base = 16(3.14) = 50.24 inches²

∵ The area of the curved surface = 2πrh

∵ r = 4 inches and h = 9 inches

∴ The area of the curved surface = 2(3.14)(4)(9) = 226.08 inches²

∴ The surface area of the cylinder = 226.08 + 50.24 = 276.32 inches²

# The surface area of the rectangular prism

∵ The dimensions of its base are 16 and 11 inches

∵ The area of the rectangle = length × width

∴ The area of the lower base = 16 × 11 = 176 inches²

∵ The area of the top face = area of the rectangle - area of the circle

∵ The area of the rectangle = 176 inches²

∵ The area of the circle = 50.24

∴ The area of the top face = 176 - 50.24 = 125.76 inches²

- There are two side faces with dimensions 16 and 11 inches

∴ The area of the two faces = 2 × 16 × 11 = 352 inches²

- There are two faces with dimensions 11 and 11 inches

∴ The area of the two faces = 2 × 11 × 11 = 242 inches²

∵ The surface area of the rectangular prism is the sum of the 6 faces

∴ The surface area of the prism = 176 + 125.76 + 352 + 242

∴ The surface area of the prism = 895.76 inches²

- The surface area of the composite figure is the sum of the surface

  area of the cylinder and the surface area of the prism

∵ The surface area of the cylinder = 276.32 inches²

∵ The surface area of the prism = 895.76 inches²

∴ The surface area of the composite figure = 276.32 + 895.76

∴ The surface area of the composite figure = 1172.08 inches²

Answer: After 1 year = $15085.85168

After 5 years = $20339.34789

After 10 years = $29549.21947

After 25 years = $90609.34284

Step-by-step explanation:

14000e^.0747 (however many years)

Answer:

The balance after 1 year, 5 years, 10 years, 25 years are 15085.85, 20339.35, 29549.22 and 90609.34 respectively.

Step-by-step explanation:

It is given that the principle amount is $14,000 and interest rate is 7.47%.

The formula for amount is

[tex]A=Pe^{rt}[/tex]

Where, P is principle, r is rate of interest and t is time in years.

Substitute P=14000 and r=0.0747 in the above equation.

[tex]A=14000e^{0.0747t}[/tex]         ..... (1)

Substitute t=1 in equation (1) to find the balance after 1 year.

[tex]A=14000e^{0.0747(1)}=15085.851678\approx 15085.85[/tex]

Substitute t=5 in equation (1) to find the balance after 5 year.

[tex]A=14000e^{0.0747(5)}=20339.3478896\approx 20339.35[/tex]

Substitute t=10 in equation (1) to find the balance after 10 year.

[tex]A=14000e^{0.0747(10)}=29549.2194696\approx 29549.22[/tex]

Substitute t=25 in equation (1) to find the balance after 25 year.

[tex]A=14000e^{0.0747(25)}=90609.3428426\approx 90609.34[/tex]

Therefore the balance after 1 year, 5 years, 10 years, 25 years are 15085.85, 20339.35, 29549.22 and 90609.34 respectively.

Answer:

Option D. 90°

Step-by-step explanation:

we have

[tex]D(5, 7),E(4, 3),F(8, 2)[/tex]

Plot the vertices

see the attached figure  

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance DE

[tex]D(5, 7),E(4, 3)[/tex]

substitute

[tex]d=\sqrt{(3-7)^{2}+(4-5)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(-1)^{2}}[/tex]

[tex]DE=\sqrt{17}\ units[/tex]

step 2

Find the distance EF

[tex]E(4, 3),F(8, 2)[/tex]

substitute

[tex]d=\sqrt{(2-3)^{2}+(8-4)^{2}}[/tex]

[tex]d=\sqrt{(-1)^{2}+(4)^{2}}[/tex]

[tex]EF=\sqrt{17}\ units[/tex]

step 3

Find the distance DF

[tex]D(5, 7),F(8, 2)[/tex]

substitute

[tex]d=\sqrt{(2-7)^{2}+(8-5)^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2}+(3)^{2}}[/tex]

[tex]DF=\sqrt{34}\ units[/tex]

step 4

The triangle DEF is a right triangle because satisfy the Pythagoras theorem

so

[tex](\sqrt{34})^{2}=(\sqrt{17})^{2}+(\sqrt{17})^{2}[/tex]

[tex]34=34[/tex] -----> is true

therefore

The measure of angle DEF is a right angle

Answer:

The combined like terms to create an equivalent expression [tex]20(-1.5r+0.75)[/tex] is [tex]-30r + 15[/tex].

Step-by-step explanation:

Consider the provided expression:

[tex]20(-1.5r+0.75)[/tex]

Use the distributive property: [tex]a(b + c) = ab + bc[/tex]

[tex]-30r + 15[/tex]

After using distribution property there are no more like terms. Thus, [tex]-30r + 15[/tex] is the simplest form.

Hence, the combined like terms to create an equivalent expression [tex]20(-1.5r+0.75)[/tex] is [tex]-30r + 15[/tex].

Based on the information, the simplified expression is -30r + 15.

Given expression:

20(-1.5r+0.75)

Applying the distributive property:

= 20(-1.5r) + 20(0.75)

= -30r + 15

Therefore, the simplified expression is -30r + 15.

Use the distributive property to distribute the 20 to each of the terms inside the parentheses.

Simplify the expression by combining the like terms.

The simplified expression is -30r + 15.

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Answer:

t = 6162 years

Step-by-step explanation:

This equation takes the form of

[tex]N=N_{0}e^{kt}[/tex]

We are given everything but the amount of C-14 at time t = 0.  But we can figure it out from the info we ARE given.  We are told that when the spear head is found it contains 54% of its original amount of C-14.  Notice we are dealing in percents.  If 54% remains when it is found, it started out with 100% of its amount.  That's our N value.  Filling in:

[tex]100=54e^{.0001t}[/tex]

Our goal is to get that t down from the exponential position that it is currently in.  To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication.  So we take the natural log of both sides.  On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone.  Before that, though, we will simplify by dividing both sides by 54.  100/54 = 1.851851852.  So, altogether...

[tex]ln(1.851851852)=.0001t[/tex]

Simplifying by plugging the log of that number into our calculator, we get

.6161861395 = .0001t  and

t = 6161.8613

Rounding to the nearest year, t = 6162 years

Answer:

D.  

individual retirement account

Step-by-step explanation:

The account that will be beneficial to Victor, to ensure he has enough funds during his old age, is the  individual retirement account(IRA).

Answer:

The most appropriate answer option is D. Individual Retirement Account.

Step-by-step explanation:

We know that Victor is a mechanic and he wants to make sure that he has enough funds during his old age.

For this purpose, an Individual Retirement Account (IRA) would be the most suitable and beneficiary for him.

An Individual Retirement Account is a type of account that is tax advantaged and aims to help people save for their post retirement life.

Answer:

$6.40

Step-by-step explanation:

We first multiply 1.20 by 3 so we can find the price for 3 parcels. We then subtract the result by 10 to get the change Late should get

10-3(1.20)

=10-3.60

=6.40

The required change is $ 6.40

So price of 3 parcels = $3(1.20) = $ 3.60

So, the change = $ {  10-3.60  }

= $ 6.40

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Answer:

Step-by-step explanation:

Please avoid use of " x " to indicate multiplication; instead, use " * " or " · "

P = ( 2 x l ) + ( 2 x w )  comes out as   P = ( 2 * l ) + ( 2 * w ).

This could be written in several different ways, e. g.,

P = ( 2 * l ) + ( 2 * w ),

P = ( 2 * w ) + ( 2 * l ),

P = ( l * 2 ) + ( w * 2), and so on.

The Distributive Property permits us to rewrite the formula P = (2 x l) + (2 x w) as P = 2(l + w). This factorization is an alternative mathematical representation of the same calculation.

Yes, you can utilize the Distributive Property to rewrite the formula P = (2 x l) + (2 x w) in a different way. The Distributive Property in mathematics is a fundamental property that states a(b + c) = ab + ac, which means you can distribute multiplication over addition. Applying this property to the formula P = 2l + 2w, we can factor out a common factor of 2 from both terms. So the formula can be written equivalently as P = 2(l + w).

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Answer:

4 1/8 inches

Step-by-step explanation:

7 1/4 - 3 1/8

(7-3) + (1/4 -1/8)

4 + (1/4 - 1/8)

4 + 1/8

4 1/8 inches

Answer:

  4 1/8 inches

Step-by-step explanation:

You apparently want to find the sum (in inches) ...

  5.5 + (1 3/4) - (3 1/8)

This can be done a number of ways. One is to use an appropriate calculator.

__

Another way to do this is to add the integer parts and fraction parts separately:

  = (5 +1 -3) +(1/2 +3/4 -1/8)

  = 3 + (4/8 +6/8 -1/8) = 3 + (4+6-1)/8 = 3 9/8

  = 4 1/8

__

Another way is to convert all the numbers to decimal, then add.

  = 5.500 +1.750 -3.125

  = 7.250 -3.125

  = 4.125 = 4 1/8

__

There were 4 1/8 inches of snow remaining Tuesday evening.

Answer:

Step-by-step explanation:

Let k represent the pounds of produce coming from Kelsey's garden. Then Doug's garden produces 5.8k pounds of produce, and the total weight of it is ...

  k + 5.8k = 102

  6.8k = 102 . . . . . . . . . . . simplify

  k = 102/6.8 = 15 . . . . . . pounds of produce from Kelsey's garden

  5.8k = 5.8·15 = 87 . . . . pounds of produce from Doug's garden

Answer:

6⃣

Step-by-step explanation:

3 + 24x² + 48x⁶; take the highest degree term possible.

Answer:

degree 6

Step-by-step explanation:

To obtain (f ￮ g(x) substitute x = g(x) into f(x)

f(4x³ + 1)

= 3(4x³ + 1)²

= 3(16[tex]x^{6}[/tex] + 8x³ + 1)

= 48[tex]x^{6}[/tex] + 24x³ + 3

The degree is determined by the term with the largest exponent.

In this case 48[tex]x^{6}[/tex] ← with exponent 6

Hence the polynomial is of degree 6

Answer:

[tex]19.22\:<\:\mu\:<\:44.78[/tex]

Step-by-step explanation:

Tthe population is normally distributed and the sample size is [tex]n=22\:<\:30[/tex].

Since the population standard deviation [tex]\sigma[/tex] is unknown and the sample standard deviation [tex]s[/tex], must replace it, the t distribution must be used for the confidence interval.

Hence with degrees of freedom of 21, [tex]t_{\frac{\alpha}{2} }=3.527[/tex].(Read from the t distribution table)

The 98% confidence interval can be constructed  using the formula:

[tex]\bar X-t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )\:<\:\mu\:<\:\bar X+t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )[/tex].

From the question the sample mean is [tex]\bar X=32[/tex]dollars and the sample standard deviation is [tex]s=17[/tex] dollars.

We substitute the values into the formula to get

[tex]32-3.527(\frac{17}{\sqrt{22} } )\:<\:\mu \:<\:32+3.527(\frac{17}{\sqrt{22} } )[/tex]

[tex]19.22\:<\:\mu\:<\:44.78[/tex]

Therefore, we can be 98% confident that the population mean is between is between 19.22 and 44.78 dollars.

Answer:

Step-by-step explanation:

D

Answer:

193

Step-by-step explanation:

We need to convert the decimal part of that number from years to days.  Do that like this:

.52895 × [tex]\frac{365days}{1year}[/tex].

The year label cancels and we are left to multiply .52895 by 365 to get 193.06675 days.

Final answer:

3.52895 years is approximately 3 years and 193 days when converted, using the average number of days in a year (365.2422) to calculate the days from the fractional part of the year.

Explanation:

To calculate the time in years and days when given a decimal of years, one must convert the fractional part of the year into days. Assuming that the initial figure 'If = 3.52895' represents 3.52895 years, we would have 3 complete years and a fraction of a year (0.52895). To find the number of days in this fractional year, we need to multiply it by the average number of days in a year. The average year contains 365.2422 days, accounting for the additional leap year day every four years.

To convert the 0.52895 of a year to days, the calculation would be:

0.52895 × 365.2422 = 193.215 (approximately).

Therefore, 3.52895 years is roughly 3 years and 193 days.

Answer:

1. 0.1367

2. 0.0709

3. 0.1766

Step-by-step explanation:

The probability of success is p=0.6, then the probability of a failure is q=1-0.6=0.4.

1. The probability that there are exactly 13 successes in 24 trials is

[tex]C^{24}_{13}p^{13}q^{24-13}=\dfrac{24!}{13!(24-13)!}\cdot (0.6)^{13}\cdot (0.4)^{11}\approx 0.1367[/tex]

2. The probability that there are exactly 9 successes in 20 trials is

[tex]C^{20}_{9}p^{9}q^{20-9}=\dfrac{20!}{9!(20-9)!}\cdot (0.6)^{9}\cdot (0.4)^{11}\approx 0.0709[/tex]

3. The probability that there are exactly 6 failures in 12 trials is

[tex]C^{12}_{6}q^{6}p^{12-6}=\dfrac{12!}{6!(12-6)!}\cdot (0.4)^{6}\cdot (0.6)^{6}\approx 0.1766[/tex]

Answer:

The metric system is a called a decimal-based system because it is based on multiples of ten.

Answer:

20

Step-by-step explanation:

The two given and marked angles add up to 90.

A = x

B = 3x + 10

A + B = 90          Substitute for A and B. A and B are just letters I gave things.

x + 3x + 10 = 90        Combine the left

4x + 10 = 90              Subtract 10 from both sides.

4x +10-10 = 90-10     Combine

4x = 80                      Divide by 4

4x/4=80/4

x = 20

Answer:

x=20

Step-by-step explanation:

The two angles are complementary angles.  Complementary angles add to 90 degrees

x + 3x+10 = 90

Combine like terms

4x+10 = 90

Subtract 10 from each side

4x+10-10 = 90-10

4x= 80

Divide each side by 4

4x/4 = 80/4

x = 20

Answer:

The sample should be a random sample from the entire set of students and should include enough students to be reliable. Small samples have more variation, which leads to less reliable inferences.

To find out how many sixth through eighth grade students are interested in joining a running club, you can conduct a survey among these students. Choose a sample by randomly selecting a certain number of students from the list, ensuring diversity. Contact the selected students to ask about their interest in joining the club and calculate the percentage of interested students.

To find out how many sixth through eighth grade students are interested in joining a running club, you would need to conduct a survey or questionnaire among the students in these grades. Here's how you can choose a sample that will give you a good representation of the whole population: