Considering the expression of a line, the equation of the line that passes through the pair of points (-3,5) and (1,-1) is y=-1.5x +0.5.
Definition of linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope and the value of one of the points, the value of the ordinate to the origin can be obtained.
Equation in this caseIn this case, being (x₁, y₁)= (-3, 5) and (x₂, y₂)= (1, -1), the slope m can be calculated as:
m= ( -1 -5)÷ (1 - (-3))
m= ( -1 -5)÷ (1 + 3)
m= (-6)÷ 4
m= -1.5
Considering point 2 and the slope m, you obtain:
-1= -1.5×1 + b
-1= -1.5 +b
-1 + 1.5= b
0.5= b
Finally, the equation of the line is y=-1.5x +0.5.
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PLEASEEEE HELP ME I NEEEED AN EXPERT TO DO THIS ):
Answer: B
Step-by-step explanation:
Answer:
The answer is B) -35.16 grams per half-life cycle
How do you find the area of this shaded shape? Thank you!
Answer:
1,760m
Step-by-step explanation:
The side of the smaller triangle is multiplied by 4, which got 44 in the bigger triangle. So you would multiply the base of the smaller by 4 as well, resulting in 80. Now you need to multiply the base and the side of the triangle, and divide that answer by half.
FORMULA FOR A TRIANGLE:
A= 1/2( L x W )
A= 1/2 (44 x 80)
A= 1/2 (3520)
A= 1760
Therefore, the area of the shaded triangle is 1,760m.
SORRY IF THIS DID NOT MAKE SENSE!
Juanita covered the outside of a gift box shaped like a rectangular prism with the paper. The box is 3. 2 feet long and 2. 1 feet wide and 2. 7 feet high what could be the closest to the total to the surface area
The total surface area of a gift box is 42.06 square feet
We know that the formula for the surface area of rectangular prism is:
A = 2(lw + wh + lh)
where l is the length
w is the width
and h is the height
The box shaped like a rectangular prism is 3.2 feet long and 2.1 feet wide and 2.7 feet high.
⇒ l = 3.2 ft,
w = 2.1 ft
and h = 2.7 ft
Using above formula the total surface area of the box would be,
A = 2(lw + wh + lh)
A = 2 × [(3.2 × 2.1) + (2.1 × 2.7) + (3.2 × 2.7)]
A = 2 × 21.03
A = 42.06 square feet
Therefore, the required area is 42.06 square feet
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will give brainliest to first answer
Answer:
the answer to your question is x=3
Answer:
Option A: x = 3
Step-by-step explanation:
The lowest part of the parabola has an x-value of 3.
A grocery store finds that the number of boxes of new cereal sold increases each week. In the 1st week, 24
boxes of cereal were sold. In the 2nd week, 39 boxes of cereal were sold and in the 3rd week 54 boxes of
cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.
A) Write the explicit rule in simplified form for the arithmetic sequence that defines the number of boxes
of cereal sold in week n. Make sure to show all steps
B) Use this rule to calculate how many boxes of cereal will be sold during the 10th week.
Answer: a)159 boxes of cereal will be sold during the 10th week, b) an = 15n + 9
Step-by-step explanation:
Solve the differential equation.
dy/dx = 9x2y2
for y\neq0
The general solution to the differential equation is y = -1/(3x³ + C)
Where C is an arbitrary constant.
Solving the differential equation:
The concept used to solve this differential equation is the separation of variables. Separated the variables on either side of the equation and then integrated both sides to get the general solution with a constant of integration.
Note that, the solution is valid only for y ≠ 0 as the differential equation is undefined for y = 0.
Here we have
dy/dx = 9x²y²
Solve the differential equation using the separation of variables.
=> dy/dx = 9x² y²
Let's separate the variables by dividing both sides by y² and dx:
=> 1/(y²) dy = 9x² dx
Now we can integrate both sides:
=> ∫1/(y²) dy = ∫9x² dx
Using the power rule of integration, we get:
=> -1/y = 3x³ + C
Where C is the constant of integration.
To solve for y, we can multiply both sides by -1:
=> y = -1/(3x³ + C)
Therefore,
The general solution to the differential equation is y = -1/(3x³ + C)
Where C is an arbitrary constant.
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Help please need answers now (with solutions too please)
The probability of drawing two hearts without replacement is 0.0588. The probability of drawing an ace followed by a king without replacement is 0.006.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. Usually, it is stated as a number between 0 and 1, where 0 denotes that an event is impossible and 1 denotes that it is certain to happen.
According to question:6) To find the probability of drawing two hearts without replacement, we can use the formula:
P(two hearts) = (number of ways to choose 2 hearts) / (number of ways to choose 2 cards from a deck)
As there are 13 hearts in a standard deck of 52 cards, the number of ways to choose 2 hearts is given by the combination:
13 choose 2 = 13! / (2! * (13-2)!) = 78
The number of ways to choose 2 cards from a deck of 52 cards is:
52 choose 2 = 52! / (2! * (52-2)!) = 1326
Therefore, the probability of drawing two hearts without replacement is:
P(two hearts) = 78 / 1326 ≈ 0.0588 (rounded to four decimal places)
7) To find the probability of drawing an ace followed by a king without replacement, we can use the formula:
P(ace, then king) = P(ace) * P(king|ace not drawn)
The probability of drawing an ace is given by:
P(ace) = 4/52 = 1/13
After drawing an ace from the deck, there are 51 cards remaining, of which 4 are kings. Therefore, the probability of drawing a king given that an ace has not been drawn is:
P(king|ace not drawn) = 4/51
Hence, the probability of drawing an ace followed by a king without replacement is:
P(ace, then king) = (1/13) * (4/51) ≈ 0.006 (rounded to three decimal places).
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please help me out on this question! (i will give u brainiest)
Answer:
4(6) + 4(5) + 4(4) = 24 + 20 + 16 = 60 ft^2
two different missiles are shot simultaneiously at a practice target. if the probability of the first one hitting the target is 1 4 and of the second one hitting is 2 5 , what is the probability that (a) both missiles will hit, (b) at least one will hit?
(a) The probability that both missiles will hit the target is 1/10.
(b) The probability that at least one missile will hit the target is 11/20.
To find the probability that both missiles will hit, we multiply the individual probabilities of each missile hitting
P(both missiles hit) = P(first missile hits) × P(second missile hits)
P(both missiles hit) = (1/4) × (2/5)
P(both missiles hit) = 2/20
P(both missiles hit) = 1/10
So the probability that both missiles will hit the target is 1/10.
(b) To find the probability that at least one missile will hit, we need to find the probability that both missiles miss and then subtract that from 1 (since the probability of either missile hitting is the complement of both missiles missing)
P(at least one missile hits) = 1 - P(both missiles miss)
P(at least one missile hits) = 1 - P(first missile misses) × P(second missile misses)
P(at least one missile hits) = 1 - (3/4) × (3/5)
P(at least one missile hits) = 1 - 9/20
P(at least one missile hits) = 11/20
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PLEASE HELP and add a photo of your work and explain how you got the answer. I WILL MARK YOU BRAINLIEST IF YOU DO!! thanks!
The coordinates for the dilated figure would be A'(-2, 2), B'(-2, -1), C'(2, -1), and D'(2, 2).
The kind of dilation that was done is called a reduction.
What is a reduction dilation ?When you dilate a figure with a scale factor k = 1/3, you are performing a reduction, because the scale factor is between 0 and 1. In this case, the dilation will shrink the original figure by a factor of 1/3.
To find the coordinates of the dilated points, multiply the x and y coordinates of each point by the scale factor (1/3):
A' = (-6 x 1/3, 6 x 1/3) = (-2, 2)
B' = (-6 x 1/3, -3 x 1/3) = (-2, -1)
C' = (6 x 1/3, -3 x 1/3) = (2, -1)
D' = (6 x 1/3, 6 x 1/3) = (2, 2)
The coordinates of the dilated figure are A'(-2, 2), B'(-2, -1), C'(2, -1), and D'(2, 2). This type of dilation is a reduction, as the figure becomes smaller.
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Nathan is making lemonade to sell at a school fundraiser. His recipe requires $4 times as much water as sugar and twice as much sugar as lemon juice. He uses $3 cups of lemon juice. How many cups of water does he need
Nathan needs 24 cups of water to make his lemonade recipe.
Let's call the amount of lemon juice Nathan uses "x".
We know that Nathan uses 3 cups of lemon juice, so we can substitute x = 3 into the problem.
According to the recipe, the amount of sugar Nathan needs is twice the amount of lemon juice, so he needs 2x cups of sugar.
Substituting x = 3, we get that Nathan needs 2(3) = 6 cups of sugar.
The amount of water Nathan needs is four times the amount of sugar he needs, so he needs 4 times 6 cups of water, which is equal to 24 cups of water.
Therefore, Nathan needs 24 cups of water to make his lemonade recipe.
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The table shows the cost, c, of making different numbers of shirts, t. Create an equation to model the cost. Number of Shirts, t 100 250 500
Cost to Company, c $600. 00 $1,387. 50 $2,700. 00
Equation __
The equation models the cost of making different numbers of shirts, where y is the cost in dollars and x is the number of shirts produced is y = 7.5x - 750
To create an equation that models the cost of making different numbers of shirts, we need to determine the relationship between the number of shirts produced and the cost. One way to do this is to use the two-point form of the equation of a line, which is:
y - y₁ = (y₂ - y₁)/(x₂ - x₁) * (x - x₁)
where (x₁, y₁) and (x₂, y₂) are two points on the line.
Using the points (100, 600) and (250, 1387.50), we can find the slope of the line:
slope = (y₂ - y₁)/(x₂ - x₁) = (1387.50 - 600)/(250 - 100) = 7.5
Then, we can use the point-slope form of the equation of a line to write the equation:
y - y₁ = m(x - x₁)
where m is the slope and (x1, y1) is a point on the line. Using the point (100, 600), we get:
y - 600 = 7.5(x - 100)
Simplifying, we get:
y = 7.5x - 750
This equation models the cost of making different numbers of shirts, where y is the cost in dollars and x is the number of shirts produced.
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PLEASE HELP! PHOTO ATTACHED
The height of a cabinet is twice the width. The depth is 1.5 times the width. The volume of the cabinet is 5.184 in^3. What are the dimensions of the cabinet?
Answer: Width: 12 Height: 24 Depth: 18
Step-by-step explanation: Width= 12, 12x2=24 and 12x1.5=18. 12x24x18=5184in3
sweets are sold loose,or pre-packed in 120g bags
Step-by-step explanation:
The option that has the better value is the loose sweets.
What is division?
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
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Which pack has the better value?
Price per gram for the bag = £1.49 / 120 = £0.0124
Price per gram for the loose sweets = £0.89 / 100 = £0.0089
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one box contains 4 green balls and 3 red balls. another box contains 4 redballs and 3 purple balls. a box will be selected at random, then two balls willbe randomly selected from that box without replacement. if the first ball isred, what is the probability that the second ball also will be red? express youranswer as a common fraction and sum the numerator and denominator.
The probability of drawing two red balls in a row from one of the two boxes, given that the first ball drawn is red, is 1/7.
The first step in solving this problem is to determine the probability of selecting the red box versus the other box. Since we have two boxes and each one has an equal chance of being selected, the probability of selecting the red box is 1/2.
Now we can put all of these probabilities together to determine the overall probability of drawing two red balls in a row from one of the two boxes.
We know that the probability of selecting the red box is 1/2, the probability of drawing a red ball on the first try is 4/7, and the probability of drawing a red ball on the second try, given that we've already drawn one red ball, is 1/2.
To find the overall probability, we simply multiply these three probabilities together:
(1/2) x (4/7) x (1/2) = 1/7
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The probability that the second ball will be red, given that the first ball is red, is 3/7.
Explanation:To find the probability that the second ball will also be red given that the first ball is red, we need to consider two cases.
Case 1: Selecting a box with 4 red balls and 3 purple balls.
The probability of selecting a red ball from this box is 4/7. Since we are drawing without replacement, the probability of selecting another red ball is 3/6.Case 2: Selecting a box with 4 green balls and 3 red balls.
The probability of selecting a red ball from this box is 3/7. Since we are drawing without replacement, the probability of selecting another red ball is 2/6.Now, we calculate the overall probability by adding the probabilities of the two cases: (4/7) * (3/6) + (3/7) * (2/6) = 12/42 + 6/42 = 18/42 = 3/7.
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Find the value of x in the figure below.
Answer:
x = 63° and y =153°
Step-by-step explanation:
a streght line measure 180° so in the given we sum up
90° + x + 27°=180° then solve x
and for y u will sum up 90° and x then u will get by vertical opposite angle
A rental company charges a flat fee of $50 to rent a ski jet. In addition, renters must pay $17.50 per hour of ski use. Which equation correctly represents the total cost, c, to rent a jet ski for h hours?
Answer:
f(x) C= x+50 x=17.50$/h
Step-by-step explanation:
I might not be sure about it, but it might be a function that is f(x) C= x + 50 dollars
x=17.50 dollars /hour
so that means if it is 1 hour, then 17.50$ +50$ which is 67.50$, if it's 2 hours then 17.50$/h = n$/2h so n=17.50$ *2 = 35$ + 50$ = 85$
A restaurant offers 18 types of pizza. A small cafe offers 1/3 as many types of pizza. How many fewer types of pizza does the small cafe offer?
Answer:
6 fewer pizzas
Step-by-step explanation:
The small cafe offers 6 fewer types of pizza than a restaurant. The restaurant offers 18 different types of pizzas and the cafe offers 1/3 as many types of pizzas which means what we have to find 1/3 of 18.
1/3 of 18 is 6 because 6*3 is 18
18 - 6 = 12 which is the number of pizzas the cafe offers but this is slightly irrelevant to the question because the question is asking how many FEWER pizzas the cafe sells than the restaurant
So, the small cafe offers 6 FEWER pizzas than the restaurant.
Hope this helps!
You toss a coin 50 times and observe 35 heads. You can conclude that:Question 4 options:a) this coin is not fair, but is weighted to land heads-up.b) the true probability of getting a head on any random flip of this coin could be far from 0.70.c) the probability of getting a head on any random flip of this coin is 0.70.d) you are not very good at coin-flipping since you should get 25 heads if you're doing it correctly.
Answer: its b
Step-by-step explanation: all coins have a heads and tails so that takes out c.
d is just for jokes
a. a coin in a school problem is not gonna be wieghted.
The radius of a circle is 8 inches. What is the angle measure of an arc bounding a sector with area 8pi square inches?
K = 8pi sq. in
r = 8 in
Give the exact answer in simplest form.
The angle measure of the arc bounding the sector with area 8π square inches is 45 degrees.
What is area of the sector?The area of the sector is given by the formula:
[tex]A = (1/2) r^2[/tex]θ
where A is the sector's area, is the sector's central angle in radians, and r is the circle's radius.
The radius of the circle is 8 inches, and the area of the sector is 8 square inches. When these values are added to the formula, we get:
8π = [tex](1/2) (8^2)[/tex] θ
Simplifying, we get:
8π = 32θ
Dividing both sides by 32, we get:
θ = π/4 radians
To convert this to degrees, we multiply by 180/π:
θ = (π/4) × (180/π) = 45 degrees
As a result, the angle of the arc that divides the 8-square-inch sector is 45 degrees..
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50 POINTS
A study was conducted to investigate whether local car mechanics charge women more than men for a transmission repair. The researcher selected randomly one man and one woman from everyone who had used the same mechanic for the same transmission repair. The process was repeated for a total of seven selected randomly cars. The repair prices and the differences are shown in the table.
Car 1 Car 2 Car 3 Car 4 Car 5 Car 6 Car 7
Women $3,550 $3,200 $1,850 $2,000 $3,000 $1,950 $2,250
Men n $3,285 $3,100 $1,975 $2,150 $2,850 $1,750 $2,175
Difference$265 $100 −$125 −$150 $150 $200 $75
Mean Standard Deviation
Women $2,542.86 $691.27
Men $2,469.29 $599.77
Difference $73.57 $157.37
Dotplots of the data and the differences are shown.
(image)
Do the data provide convincing statistical evidence that women pay more than men for the same transmission repair?
we do not have convincing statistical evidence that women pay more than men for the same transmission repair
How to determine if data provide convincing statistical evidence that women pay more than men for the same transmission repairTo determine whether the data provide convincing statistical evidence that women pay more than men we do not have convincing statistical evidence that women pay more than men for the same transmission repair for the same transmission repair, we can perform a hypothesis test.
Null hypothesis: The mean repair cost for women is the same as the mean repair cost for men.
Alternative hypothesis: The mean repair cost for women is greater than the mean repair cost for men.
We can use a two-sample t-test for the difference in means, assuming equal variances.
The test statistic is given by:
t = (xbar1 - xbar2) / (s_p * sqrt(1/n1 + 1/n2))
where xbar1 and xbar2 are the sample means, s_p is the pooled standard deviation, and n1 and n2 are the sample sizes.
The degrees of freedom is given by:
df = n1 + n2 - 2
Using the data given, we have:
xbar = 2542.86, xbar2 = 2469.29
s1 = 691.27, s2 = 599.77
n1 = n2 = 7
First, we can calculate the pooled standard deviation:
s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1 + n2 - 2))
s_p = sqrt(((6)*691.27^2 + (6)*599.77^2) / (7 + 7 - 2))
s_p = 644.47
Then, we can calculate the t-statistic:
t = (xbar 1 1 - xbar2) / (s_p * sqrt(1/n1 + 1/n2))
t = (2542.86 - 2469.29) / (644.47 * sqrt(1/7 + 1/7))
t = 0.97
Using a t-distribution table with df = 12 and a significance level of 0.05, the critical value for a one-tailed test is 1.7823. Since our t-statistic is less than the critical value, we fail to reject the null hypothesis.
Therefore, we do not have convincing statistical evidence that women pay more than men for the same transmission repair
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please i need your help for today please i would really appreciate it
Answer:$8.99
Step-by-step explanation:
find the lemgth of arc PQ
The arc length is D) 3.14 meters.
What is arc length?
In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.
It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.
The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.
[tex]A_L=\frac{\theta}{360\textdegree}2\pi r[/tex]
Here the give circle Radius PR = 3m and θ=60°.
Now using arc length formula then,
=> Arc length [tex]A_L=\frac{\theta}{360\textdegree}2\pi r[/tex]
=> [tex]A_L=\frac{60}{360} \times2\times3.14\times3[/tex]
=> [tex]A_L=\frac{1}{6}\times2\times3.14\times3[/tex]
=> [tex]A_L[/tex] = 3.14 m.
Hence the arc length is D) 3.14 meters.
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You work for a lender that requires a 15% down payment and uses the standard debt-to-income ratio to determine a person's eligibility for a home loan. Of the following, choose the person that you would rate the highest on their eligibility for a home loan.
Person A
Person B
Person C
Person D
home value
$95,000
$107,000
$120,000
$128,000
income
$46,000
$53,000
$58,000
$60,000
savings
$20,000
$13,910
$18,000
$19,200
recurring debt
$310
$198
$265
$400
a.
Person A
b.
Person B
c.
Person C
d.
Person D
Person C would rate the highest on their eligibility for a home loan.
What is a down payment?A down payment is a payment made upfront by a buyer when purchasing a big-ticket item, such as a house or a car.
It is typically a percentage of the total purchase price, and the remaining balance is financed through a loan.
We have,
Debt-to-income ratio for each person:
Person A:
Down payment = $14,250, Debt-to-income ratio = ($310 / $3,833) x 100% = 8.08%
Person B:
Down payment = $16,050. Debt-to-income ratio = ($198 / $4,416) x 100% = 4.49%
Person C:
Down payment = $18,000. Debt-to-income ratio = ($265 / $4,833) x 100% = 5.49%
Person D:
Down payment = $19,200. Debt-to-income ratio = ($400 / $5,000) x 100% = 8.00%
Now,
Based on these calculations, Person C has the highest down payment and the lowest debt-to-income ratio, making them the most eligible for a home loan.
Therefore,
Person C would rate the highest on their eligibility for a home loan.
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Based on the graphs of the two functions, which statement is true?
Answer:f(4)=g(4)
Step-by-step explanation:We see that when x= 4, we see that f(4) intersects g(4)
The median of distribution A is 8. which of these could be the mean?
a. 7
b. 8
c. 9
d. It cant be determined
Answer:
Step-by-step explanation:
The mean of the distribution with a median of 8 could also be: Option B: 8
How to interpret the mean, median and mode?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is defined as the middle value when a data set is ordered from least to greatest.
The mode is defined as the number that occurs most often in a data set.
Now, one good relationship between the 3 measures is given as:
3(median) = mode +2(mean)
Thus, if our median is 8, then it is very possible that our means could also be 8
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A quadratic function is defined by ƒ (x) = x² + 5x − 24.
Which of the following expresses ƒ (x) as the product of
two linear factors?
A
B
C
ƒ (x) = (x − 4) (x + 6)
f(x) = (x − 3)(x + 8)
f(x) = (x + 3) (x − 8)
D fl
f(x) = (x + 4) (x - 6)
please be correct :/
Question 12
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Question 13
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 14
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Answer:
I already did this go check the answers on the other one
Step-by-step explanation:
Find the surface area of the pyramid.
PLEASE HELP I HAVE TO SUBMIT THIS SOON AND I CANT FIGURE IT OUT
The surface area of the pyramid is approximately 721.04 square feet.
Describe Area?Area is a measure of the size of a two-dimensional region or surface, such as a rectangle, triangle, circle, or any other shape. It is the amount of space inside the boundaries of a closed figure, expressed in square units. The unit of measurement used for area depends on the context and the system of measurement being used, but some common units include square meters, square centimeters, square feet, and square inches.
To calculate the area of a regular shape, such as a square or rectangle, you can multiply the length of the base by the height or width of the shape. For more complex shapes, such as triangles or circles, different formulas can be used depending on the properties of the shape. Area is an important concept in geometry, as well as in many other areas of mathematics, science, engineering, and everyday life.
To find the surface area of the pyramid, we need to find the area of each face and add them up.
Since the base of the pyramid is a square, and the length of each side is 13 ft, the area of the base is:
Area of base = (13 ft) x (13 ft) = 169 sq ft
To find the area of each triangular face, we first need to find the slant height of the pyramid. The slant height is the distance from the apex of the pyramid to the midpoint of one of the sides of the base. We can use the Pythagorean theorem to find the slant height:
Slant height = √( (1/2 x 13 ft)² + 18 ft² )
= √( 169 ft² + 324 ft² )
= √493
≈ 22.18 ft
Now we can find the area of each triangular face using the formula:
Area of triangle = (1/2) x base x height
where the base is one of the sides of the square base, and the height is the slant height we just found. Therefore, the area of each triangular face is:
Area of triangle = (1/2) x 13 ft x 22.18 ft
≈ 143.01 sq f
Since there are four triangular faces, the total surface area of the pyramid is:
Total surface area = 4 x Area of triangle + Area of base
= 4 x 143.01 sq ft + 169 sq ft
≈ 721.04 sq ft
Therefore, the surface area of the pyramid is approximately 721.04 square feet.
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Javae got $100 for his birthday. He listened to a Podcast about investing, and decided he would try it. He invested his $100 into a fund that has 9% growth per year. How much will Javae have in that account on his 30th birthday? (16 years
from now).
O 1,327
O $22
O $2,884,414
O $397
Answer:
The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = $100, r = 9% = 0.09, n = 1 (compounded annually), and t = 16. We want to find A.
A = 100(1 + 0.09/1)^(1*16)
A = $397.42
Therefore, Javae will have $397.42 in his account on his 30th birthday. The answer is option D.