From the given data, the test statistic is -2.052 and the p-value is 0.0461. The correct answer is option 5.
To perform a two independent samples t-test, we can use the following formula to calculate the test statistic:
t = (x₁ - x₂) / (s_p × √(1/n₁ + 1/n₂))
where x₁ and x₂ are the sample means, n₁ and n₂ are the sample sizes, s_p is the pooled standard deviation, calculated as:
s_p = √(((n₁ - 1) × s₁² + (n₂ - 1) × s₂²) / (n₁ + n₁ - 2))
Let's calculate the test statistic:
x₁ = 60.345, s₁ = 10.8968, n₁ = 25
x₂ = 67.635, s₂ = 12.936, n₂ = 20
s_p = √(((25 - 1) × 10.8968² + (20 - 1) × 12.936²) / (25 + 20 - 2)) = 11.8074
t = (60.345 - 67.635) / (11.8074 × √(1/25 + 1/20)) = -2.052
The degrees of freedom for the t-distribution can be calculated as:
df = n₁ + n₂ - 2 = 43
Using a two-tailed t-test at a significance level of 0.05, the critical t-value is ±2.016.
The p-value for the test is the probability of obtaining a t-value as extreme or more extreme than the calculated t-value, assuming the null hypothesis is true. Since the calculated t-value is outside the critical region (|t| > 2.016), the p-value is less than 0.05 and we can reject the null hypothesis in favor of the alternative hypothesis.
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Question
Does the equation demonstrate closure of polynomials under addition?
(2x2+x)+(4x−3)=2x2+5x−3
Responses
Yes. The equation shows that the sum of the two polynomials is a polynomial. This demonstrates that polynomials are closed under addition.
Yes. The equation shows that the sum of the two polynomials is a polynomial. This demonstrates that polynomials are closed under addition.
Yes. The equation shows that the sum of the two polynomials is not a polynomial. This demonstrates that polynomials are closed under addition.
Yes. The equation shows that the sum of the two polynomials is not a polynomial. This demonstrates that polynomials are closed under addition.
No. The equation shows that the sum of the two polynomials is a polynomial. This demonstrates that polynomials are not closed under addition.
No. The equation shows that the sum of the two polynomials is a polynomial. This demonstrates that polynomials are not closed under addition.
No. The equation shows that the sum of the two polynomials is not a polynomial. This demonstrates that polynomials are not closed under addition.
Answer: yes
Step-by-step explanation:
1. The table shows the average price (in dollars) of jeans sold at different stores and the number of pairs
of jeans sold at each store in one month.
40
Average Price 22 28 35 46
a List the ordered pairs from the table and plot them
Number Sold
152
94
on a coordinate plane.
134 110 81
b. Describe the form and direction of the scatterplot
created
c. Describe the relationship between the average price of jeans and number of jeans sold.
The ordered pairs from the table are (22, 152), (28, 94), (35, 134), and (46, 110). Plotting them on a coordinate plane would produce a scatterplot.
The form of the scatterplot is a line of negative slope that is decreasing from left to right. The direction of the scatterplot is downward.
The relationship between the average price of jeans and number of jeans sold appears to be negative, which means that as the average price of jeans increases, the number of jeans sold decreases. In other words, there is an inverse relationship between the price and quantity demanded of jeans. This relationship is consistent with the law of demand in economics, which states that as the price of a good or service increases, the quantity demanded of that good or service will decrease, ceteris paribus (all else being equal).
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Return to the simpler regression specification in part (a). We want see if the deter-minants of life expectancy are different for rich and poor countries. Use membershipin the ""Organization of Economic Cooperation & Development"" (oecd) as the indica-tor of a rich country. The OECD had 30 member countries during this time period. Perform a test of the hypothesis that all three of the coefficients in the populationregression are equal for OECD and non-OECD countries. [Hint: you do not need toperform this test using factor variables. ]
We can use a two-way ANOVA to compare the means of the three coefficients for OECD and non-OECD countries and assess whether the differences are probability significant.
To test the hypothesis that the three coefficients in the population regression are equal for OECD and non-OECD countries, we can run a two-way ANOVA. The two factors in this ANOVA would be OECD status (OECD or non-OECD) and the three coefficients in the population regression (income, population density, and urbanization). This will enable us to compare the means of the three coefficients for OECD and non-OECD countries and assess whether the differences are statistically significant. We can also use the F-statistic to see if the differences between the means of the two groups are statistically significant. This will allow us to assess whether the coefficients in the population regression are indeed different for OECD and non-OECD countries.
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Find the coefficient of x/8+4=6
Answer: 0
Step-by-step explanation:
To find the coefficient of x in the equation:
x/8 + 4 = 6
We can begin by isolating x on one side of the equation. We can do this by subtracting 4 from both sides:
x/8 = 2
Next, we can multiply both sides by 8 to get rid of the fraction:
x = 16
Since there is no x-term on one side, the coefficient of x is 0.
Therefore, the coefficient of x in the given equation is 0.
Will the following variables have positive correlation, negative correlation, or no correlation? number of doctors on staff at a hospital and number of administrators on staff Will these variables have positive correlation, negative correlation, or no correlation?
There is no definitive answer to whether the variables have positive correlation, negative correlation, or no correlation.
What is a negative correlation?
A negative correlation is a relationship between two variables in which they move in opposite directions. This means that when one variable increases then the other variable decreases. In statistical terms, a negative correlation is indicated by a negative correlation coefficient, which measures the strength and direction of the relationship between two variables.
Now,
The correlation between the number of doctors on staff at a hospital and the number of administrators on staff can vary depending on the specific circumstances of the hospital.
In general, one might expect that as the number of doctors on staff increases, the demand for administrative support may also increase. In this case, we would expect a positive correlation between the number of doctors and administrators.
On the other hand, if the hospital is focused on reducing costs and improving efficiency, it may choose to reduce administrative staff while maintaining the same number of doctors. In this case, we would expect a negative correlation between the number of doctors and administrators.
Therefore, there is no definitive answer to whether the variables have positive correlation, negative correlation, or no correlation, as it depends on the specific context and factors influencing the hospital's staffing decisions.
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Write a quadratic function that has vertex in the third quadrant
and has no x-intercept, Explain how your find such function.
Quadratic function that has vertex in the third quadrant and has no x-intercept is f(x) = 2(x+3)² - 4.
Quadratic function is a polynomial function of the second degree of the form f(x)= ax² + bx + c where a is a non-zero coefficient and x is the variable. Vertex is the point on the parabola which has a minimum or maximum point. The third quadrant is where both the x and y coordinates are negative. The question requires finding a quadratic function with vertex in the third quadrant and has no x-intercept. Quadratic function with no x-intercept means that the graph does not cross the x-axis. Here is how to find such function: Step-by-step We can start by using the vertex form of a quadratic function. f(x) = a(x-h)² + k Where (h, k) is the vertex of the parabola. Since the vertex is in the third quadrant, h and k should be negative numbers.
Also, since the graph should not cross the x-axis, the leading coefficient (a) should be either positive or negative. If a>0, the parabola opens upwards, and if a<0, the parabola opens downwards. To find a quadratic function that has no x-intercept and has a vertex in the third quadrant, let's choose any negative value of h and k such that |k|>|h|, and a>0. For instance, let h=-3 and k=-4. Then, substituting these values in the vertex form, we get:f(x) = a(x+3)² - 4If we want the parabola to have a minimum point at the vertex, then a should be positive. We can choose any positive value of a. For example, let's take a=2. Then, the quadratic function with the required conditions is:f(x) = 2(x+3)² - 4f(x) = 2x² + 12x + 14The graph of this function has vertex (-3, -4) and does not cross the x-axis. Quadratic function that has vertex in the third quadrant and has no x-intercept is f(x) = 2(x+3)² - 4.
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What is the inverse of the function f (x) = 3(x + 2)2 – 5, such that x ≤ –2? inverse of f of x is equal to negative 2 plus the square root of the quantity x over 3 plus 5 end quantity inverse of f of x is equal to negative 2 minus the square root of the quantity x over 3 plus 5 end quantity inverse of f of x is equal to negative 2 minus the square root of the quantity x plus 5 all over 3 end quantity inverse of f of x is equal to negative 2 plus the square root of the quantity x plus 5 all over 3 end quantity
The inverse οf f(x) is y = -2 - √[(x + 5)/3]
Tο find the inverse οf a functiοn, we can swap the pοsitiοns οf x and y and sοlve fοr y.
Starting with f(x) = 3(x + 2)² - 5:
y = 3(x + 2)² - 5
Swap x and y:
x = 3(y + 2)² - 5
Sοlve fοr y:
x + 5 = 3(y + 2)²
(x + 5)/3 = (y + 2)²
±√[(x + 5)/3] = y + 2
y = ±√[(x + 5)/3] - 2
Since x ≤ -2, we can οnly use the negative square rοοt tο ensure that y is a functiοn. Therefοre, the inverse οf f(x) is y = -2 - √[(x + 5)/3]
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kareem is on the swim team. each day he swims 85 m. how far does he swim in nine days? write your answer in kilometers 
Answer:
0.765 km
Step-by-step explanation:
85*9=765 m
765/1000 to get km
0.765 km
16. A 40-ft. guy wire helps to support a tower. The wire is anchored to the ground 19 ft. from the base of
the tower. What is the measure of the angle formed between the wire and the ground, to the nearest
degree?
a.
25°
b. 65°
C.
62°
d. 28°
laual ground and the trunk is
Answer:
We can use trigonometry to solve this problem. Let θ be the angle formed between the wire and the ground. Then, using the right triangle formed by the wire, the tower, and the ground, we have:
cos θ = adjacent/hypotenuse
where the adjacent side is 19 ft. (distance from the base of the tower to the anchor point) and the hypotenuse is 40 ft. (length of the guy wire). Solving for θ, we get:
θ = cos^-1(19/40) ≈ 62°
Therefore, the measure of the angle formed between the wire and the ground is approximately 62 degrees. Answer C.
Step-by-step explanation:
For the function f(x)=5x^2+3x , evaluate and simplify f(x+h)-f(x)/h
The result of the evaluation and simplification of [tex]f(x)=5x^2+3x is f(x+h)-f(x)/h = h + 3[/tex], which is a line with a slope of 1 and a y-intercept of 3.
The function[tex]f(x)=5x^2+3x[/tex], when evaluated and simplified, is equal to [tex]f(x+h)-f(x)/h[/tex]. To calculate [tex]f(x+h)-f(x)/h[/tex], the first step is to subtract f(x) from f(x+h). This will leave us with the expression . After this, we can simplify the expression to [tex]h^2 + 3[/tex]h. Next, we divide this expression by h which will leave us with h + 3.
This means that our result is [tex]f(x+h)-f(x)/h = h + 3[/tex]. This can be visualized as a line on a graph with a slope of 1 and a y-intercept of 3. This means that as the value of x increases, the value of [tex]f(x+h)-f(x)/h[/tex]increases by 1 for every increase in x.
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The sum of interior angle of a regular polygon is 900 degrees. Find the number of sides of the polygon
Answer:
7
Step-by-step explanation:
(number of sides - 2) x 180 = sum of interior angles
(number of sides - 2) x 180 = 900
Reverse the formula.
900 / 180 = 5
5 + 2 = 7
Therefore, number of sides = 7
9. 3: Paper Folding folds Area of paper The area of a sheet of paper is 93. 5 square inches. Write an equation expressing the visible area $$a of the sheet of paper in terms of the number of times it has been folded $$n
The equation expressing the visible area an of the sheet of paper in terms of the number of times it has been folded n is a = 93.5/2^n.
Every time a sheet of paper is folded in half, the visible area is reduced by half. If the original area of the sheet of paper is A, then after the first fold, the visible area is A/2. After the second fold, the visible area is (A/2)/2 = A/4. In general, after n folds, the visible area is A/[tex]2^n[/tex].
In this problem, the original area of the sheet of paper is given as 93.5 square inches. Therefore, the equation expressing the visible area a of the sheet of paper in terms of the number of times it has been folded n is a = 93.5/[tex]2^n[/tex]. As the number of folds increases, the visible area of the sheet of paper decreases rapidly, approaching zero as n approaches infinity.
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28. Suppose in 1981 the retail price of a VCR at Sears was $1,389. 88. What would be the cost of that VCR in today’s dollars? Hint: You will need the CPI’s of both years to discover the answer
the cost of a VCR that sold for $1,389.88 in 1981 would be $3,686.12 in today's dollars, adjusted for inflation.
To calculate the cost of a VCR in today's dollars based on its cost in 1981, we need to adjust for inflation using the Consumer Price Index (CPI).
We need to find the CPI for the year 1981 and the current year. For example, let's say the CPI for 1981 is 98.3 and the CPI for the current year is 260.5.
Inflation rate = (Current year CPI / 1981 CPI) x 100
Inflation rate = (260.5 / 98.3) x 100
Inflation rate = 265.17
This means that the general price level has increased by 265.17% since 1981.
To find the cost of the VCR in today's dollars, we multiply its cost in 1981 by the inflation rate:
Cost in today's dollars = Cost in 1981 x (Inflation rate / 100)
Cost in today's dollars = $1,389.88 x (265.17 / 100)
Cost in today's dollars = $3,686.12 (rounded to the nearest cent)
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Find an equation of the line with gradient -1 and that passes through the
point (-3,0)
Submit Answer
Answer:
The equation of the line with gradient -1 that passes through the point (-3, 0) can be found using the point-slope form of a line. The point-slope form of a line is given by:
y - y1 = m (x - x1)
Where m is the gradient and (x1, y1) is a point on the line.
For this line, m = -1 and (x1, y1) = (-3, 0). Thus, the equation of the line is:
y - 0 = -1 (x - (-3))
y = -x + 3
Answer:
x + y + 3 = 0
Step-by-step explanation:
equation of line ( point slope format)
(y-y1) = m(x - x1)
they had given the point as (-3,0) on comparing with (x1, y1) and substituting the values in equation we get
y = -1(x +3)
final ans
x + y + 3 = 0
100 points please help
Answer:(9x + 10)(9x - 10)
Step-by-step explanation:
What is the volume of this composite figure? The slant height of the cone is 3. The height of the cone is approximately 1.658. Round your FINAL answer to the nearest hundredth.
514. 38 units³
514.38 units²
491.45 units3
Answer:
514.38 units²
Step-by-step explanation:
a rectangular rose garden has dimensions 5.5 feet by 3.75 feet. A rectangular vegetable garden has dimensions 13.75 feet by 6 feet. How many times as great is the area of the vegetable garden compared to the area of the flower garden? The area of the vegetable garden is times as great the area of the rose garden
Answer: 4
Step-by-step explanation:
Area of rose garden = 5.5 * 3.75 = 20.625
Area of vegetable garden = 13.75 * 6 = 82.5
To find how many times greater the area of the vegetable garden is, we simply divide 82.5 by 20.825
82.5 / 20.625 = 4
WILL MARK U brainlist!!!!!!!
Answer:
x= -12, 5
Step-by-step explanation:
im so sorry for the late response it has been a whirlwind for me with trying to graduate with school lately
zeros of a function is when f(x) is equal to zero
with the graph we can see that -12 and 5 are where f(x) is equal to zero so these are the zeros of the function
we can find this out with the equation too like this
first we find the square of the function by finding a factors of -60 that will also add to be 7
12 and -5 are 2 factors
(12)(-5)= -60
12+ -5=7
now we can use this to make 2 equations
(x+12)(x-5)=0
x+12=0
x= -12
x-5=0
x=5
I hope this helps and isn't too confusing
Find the centroid of the upper half of the circle x^2+y^2=a^2
The centroid (C) of the upper half of the circle is, C = (x_c, y_c) = (-2a/3π, 4a/3π)
We can find the centroid of the upper half of the circle by using integration. Let's denote the upper half of the circle as a function of x:
y = f(x) = sqrt(a^2 - x^2)
To find the centroid (C) of this region, we need to find the coordinates (x_c, y_c) such that:
x_c = (1/A) × ∫(a, -a) x*f(x) dx
y_c = (1/A) × ∫(a, -a) [F(x) - f(x)] dx
where A is the area of the upper half of the circle and F(x) is the equation of the circle.
First, let's find A:
A = ∫(a, -a) f(x) dx
= (1/2) × ∫(a, -a) sqrt(a^2 - x^2) dx
= (1/2) × [a^2 × sin^(-1)(x/a) + x × sqrt(a^2 - x^2)]_a^(-a)
= (1/2) × [a^2 × π + 0 - (-a^2 × π) + 0]
= πa^2/2
Next, let's find x_c:
x_c = (1/A) × ∫(a, -a) x×f(x) dx
= (2/πa^2) × ∫(a, 0) x × sqrt(a^2 - x^2) dx
(Note: We only integrate from 0 to a because the function f(x) is symmetric about the y-axis)
Let u = a^2 - x^2
Then du/dx = -2x, and dx = -du/(2x)
So the integral becomes:
(2/πa^2) × ∫(0, a^2) [(a^2 - u) × sqrt(u)] × (-du/(2x))
= -(1/πa^2) × ∫(0, a^2) sqrt(u) du
= -(1/πa^2) × [(2/3) × u^(3/2)]_0^(a^2)
= -(2/3πa^2) × (a^3)
= -2a/3π
Therefore, x_c = -2a/3π.
Finally, let's find y_c:
y_c = (1/A) × ∫(a, -a) [F(x) - f(x)] dx
= (2/πa^2) × ∫(a, 0) (a^2 - x^2) dx
(Note: We only integrate from 0 to a because the function f(x) is symmetric about the y-axis)
= (2/πa^2) × [a^2x - (1/3)x^3]_0^a
= (2/πa^2) × [(2/3)a^3]
= 4a/3π
Therefore, y_c = 4a/3π.
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Graph the function h(x) = x - 4.
Compare the graph with the graph
of f(x) = x.
Answer:
Step-by-step explanation:
these functions are both straight lines with a slope of 1
f(x) = x passes through the origin (0,0)
h(x) = x-4 is parallel to f(x) = x and passes through the y axis at (0, -4) and is below the line f(x) = x
In a 30-60-90 right triangle, the side opposite the 30- degree angle is?
Answer:
x or half the hypotenuse
Step-by-step explanation:
You can look up special triangles for more info:
Opposite 30 = x
Opposite 60 = x*(sqrt3)
Opposite 90 = 2x
the death rate from Covid19 in a certain country is 6%. what is
the probability that at least 2 patients will die out of next 10
patients
P(X≥2) = 1 - 0.389 - 0.409= 0.202. The probability that at least 2 patients will die out of next 10 patients is 0.202.
The death rate from Covid19 in a certain country is 6%. The probability that at least 2 patients will die out of next 10 patients can be found using binomial distribution. What is binomial distribution? Binomial distribution is a probability distribution that deals with the number of successes or failures in a given number of trials. A binomial distribution model is characterized by the following conditions: There are only two outcomes of the trials, either success or failure. The probability of success is constant throughout the trials.
The trials are independent of each other. The formula for the probability of binomial distribution is as follows: P(X=k) = (n C k) × p^k × (1-p)^(n-k)Where P(X=k) is the probability of k successes out of n trials. n C k represents the number of ways of selecting k items out of n items. p is the probability of success.1-p is the probability of failure. Using the above formula, the probability that at least 2 patients will die out of next 10 patients is: P(X≥2) = 1 - P(X=0) - P(X=1)P(X=0) = (10 C 0) × 0.06^0 × (1-0.06)^(10-0)= 0.389P(X=1) = (10 C 1) × 0.06^1 × (1-0.06)^(10-1)= 0.409Therefore,P(X≥2) = 1 - 0.389 - 0.409= 0.202The probability that at least 2 patients will die out of next 10 patients is 0.202.
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Sam's Sandwich Shop lets you design your own sandwich. There are 5 choices for bread, 6 choices for meat, and 4 choices for cheese. You can also choose to include (or not include ) each of the following items by request: lettuce, tomato, hot peppers, mayonnaise, or mustard.
Therefοre, the sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be the same respοnse: 3,840 pοssibilities exist.
What is an unitary methοd?The task can be cοmpleted by integrating what was learned and putting this variable technique intο practise, which alsο incοrpοrates all supplemental data frοm twο individuals whο used a specific tactic. Or, tο put it anοther way, if the desired expressiοn οutcοme happens, either the entity stated in the algοrithm will alsο be fοund, οr bοth essential prοcesses will actually bypass the cοlοur. Fοr fοrty pens, a refundable charge οf Rupees ($1.01) might be required.
Here,
⇒ [tex]$\mathrm{_n C_r=\frac{n !}{r ! (n-r) !}}[/tex]
where r is the number of chοices you select, and n is the total number of options in a category.
For instance, there are 5 οptions for bread, but you can only select 1 (since there are only 1 types of bread):
[tex]$\Rightarrow \ \mathrm{_5 C_1=\frac{5 !}{1 ! (5-1) !}}[/tex]
Similar to this, there are 6 οptions for beef, and you can only pick one:
[tex]$\Rightarrow \ \mathrm{_6 C_1=\frac{6 !}{1 ! (6-1) !}} = 6[/tex]
There are 4 options for cheese, and yοu only get to pick one:
[tex]$\Rightarrow \ \mathrm{_4 C_1=\frac{4 !}{1 ! (4-1) !}} = 4[/tex]
There are 3,840 possible sandwich cοmbos, which can be calculated using the formula
₅C₁ × ₆C₁ × ₄C₁ × 25
= 5 × 6 × 4 × 32
= 3,840
Either approach will result in the same respοnse: 3,840 possibilities exist.
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An art teacher has 4 1 8 4 8 1 gallons of paint to pour into containers. If each container holds 3 8 8 3 gallon, how many containers can they fill?
If an art teacher has 4 1/8 gallons of paint to pour into containers, the art teacher can fill 11 containers with the 4 1/8 gallons of paint they have.
To solve the problem, we need to divide the total amount of paint by the capacity of each container.
First, we need to convert 4 1/8 gallons to an improper fraction. To do this, we multiply the whole number by the denominator and add the numerator, then put the result over the denominator:
4 1/8 = (4 x 8 + 1)/8 = 33/8
Next, we divide the total amount of paint by the capacity of each container:
33/8 ÷ 3/8 = 33/8 x 8/3 = 11
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Complete question is:
An art teacher has 4 1/8 gallons of paint to pour into containers. If each container holds 3/8 gallon, how many containers can they fill?
PEMDAS
solve this using pemdas
with step by step u might want to download so u can draw on the image linked :)
Answer:
119. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Solve the equation (32
(3 % ) ( 3 ) =
X =
= 36
The value of x from the given expression (3^1/2 ) ( 3^1/2 ) = 3^6 can be expressed as 6.
How can the value of x be calculated?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists.
Given that (3^1/2 ) ( 3^1/2 ) = 3^6
then 3^(x/2+ x/2) = 3 ^6
x/2+ x/2 = 6
Then the lcm , we have
x+x/2 = 6
2x/2 = 6
2x = 12
x = 12/2 = 6
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Each of the interior angles of a regular polygon is 140 degrees. How many have it
Answer:
The polygon has 9 sides, and it is a nonagon.
Step-by-step explanation:
The formula to find the sum of the interior angles of a regular polygon is:
S = (n - 2) × 180
where S is the sum of the interior angles and n is the number of sides.
If each interior angle of the polygon is 140 degrees, we can use the formula to solve for n:
n = (S / 140) + 2
Plugging in S = 180(n-2) and simplifying, we get:
n = (180(n-2) / 140) + 2
n = (9n - 18) / 7
7n = 9n - 18
-2n = -18
n = 9
Therefore, the polygon has 9 sides, and it is a nonagon.
Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]
Does anyone know the answer to this question?
Answer:
2, -7, 3 are your answers! :).
Step-by-step explanation:
The opposite of a positive would be it's negative form, and the opposite of a negative would be it's positive form.
1. Consider the pyramid.
(a) Draw and label a net for the pyramid.
(b) Determine the surface area of the pyramid. Show your work.
(Pyramid is listed in the pdf)
2. The back of Nico’s truck is 9. 5 feet long, 6 feet wide, and 8 feet tall. He has several boxes of important papers
that he needs to move. Each box of papers is shaped like a cube, measuring 1. 5 feet on each side.
How many boxes of papers can Nico pack into the back of his truck? Show your work.
Please help!
1) The unfolded shape of solid is called the net of the solid. The net of square pyramid is present in above figure 2. Area of square pyramid is equals to 224 mm².
2) The number of boxes that fit into back of Nico’s truck is equals to the 135.
We have a pyramid with a square base and triangular faces, as shown in Figure 1 above. Length of the base of the pyramid, b = 8 mm
Height of the pyramid, h = 10 mm
The net of the square pyramid is a plan view of each face and of the square base and its dimensions. Square pyramid (5 faces), i.e., 4 triangular levels and 1 square level. Square pyramid net has total 5 unfolded faces. So, required net of square pyramid present above. Now, Surface area of square pyramid is equals to sum of area of base square and area of 4 triangular faces. So, first we determine area of base square = b² , where 'b' is side of square. Here, b =8mm so, square area A₁ = 8² = 64 mm²
Also, area of a Triangle = (1/2)× base× height
so, area of triangle = (1/2)× 8×10 = 40 mm²
Area of 4 triangular faces of pyramid, A₂
= 4× 40 = 160 mm²
Therefore, Surface area of square pyramid present above = A₁ + A₂
= 64 mm² + 160 mm² = 224 mm²
2) We have a truck with dimensions.
Length of back of Nico’s truck, l = 9.5 feet
Width of back of Nico’s truck, w = 6 feet
Height of back of Nico’s truck, l = 8 feet
He has several boxes of important papers and he wants to hold in the back of truck. The shape of each box of papers is cube. The dimensions that is side of each cube = 1.5 feet
We have to determine the number of boxes of papers Nico will pack into the back of his truck.
The volume of the truck = Length ×Width × Height = l×w×h
so, volume of the Nico’s truck = 9.5 feet × 6 feet × 8 feet = 456 feet³
Volume of box of papers ( cube) = (side)³
= (1.5 feet )³ = 3.375 feet³
Number of boxes that fit into back of truck = volume of truck/ volume of each cubic box = 456 feet³/3.375 feet³
= 456/3.375 = 135.11 ~ 135
Hence, the required number of boxes are 135.
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Complete question :
1. Consider the above pyramid, figure 1.
(a) Draw and label a net for the pyramid.
(b) Determine the surface area of the pyramid. Show your work.
(Pyramid is listed in the pdf)
2. The back of Nico’s truck is 9. 5 feet long, 6 feet wide, and 8 feet tall. He has several boxes of important papers that he needs to move. Each box of papers is shaped like a cube, measuring 1. 5 feet on each side. How many boxes of papers can Nico pack into the back of his truck? Show your work.
Please help!
Determine a series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E'?
In order to map polygon ABCDE onto polygon A'B'C'D'E', a series of transformations must be performed. A common method of transforming a figure is to use a combination of translations, reflections, rotations, and dilations.
What is transformation?Transformation of a figure is the process of changing the shape, size, position or orientation of a 2D or 3D shape. This can be done using various techniques such as translations, rotations, reflections and enlargements. The transformation of a figure can help to visualize the change and understand the different properties of the shape. It can also be used to solve mathematical problems.
A transformation is a process in which a figure is changed in size, shape, or position.
A translation is a transformation that moves a figure in any direction. To move polygon ABCDE to polygon A'B'C'D'E', one must translate the figure to the right, left, up, or down.
A reflection is a transformation that flips a figure over a line, called the line of reflection. To reflect the figure onto the new polygon, the line of reflection must be chosen.
A rotation is a transformation that turns a figure around a point, called the center of rotation. To rotate the figure onto the new polygon, the center of rotation must be chosen.
A dilation is a transformation that changes the size of a figure. To scale the figure onto the new polygon, the scale factor must be chosen.
After the transformations are applied to the original figure, it will be mapped onto the new polygon. The combination of transformations must be chosen carefully in order to achieve the desired result.
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