Answers
Hence ,the surface area of the trapezoid is 173 \(ft^{2}\) .
What is the trapezoid?In geometry, a quadrilateral with at least one set of parallel sides is referred to as a trapezium in American and Canadian English, or a trapezium in British and other forms of English. In Euclidean geometry, a trapezium is a convex quadrilateral by definition. The bases of the trapezium are the parallel sides.
What is the surface area of trapezoid?The amount of space that a trapezoidal prism is surface takes up is known as its surface area. A three-dimensional solid called a trapezoidal prism is composed of two trapezoids on opposing faces connected by four rectangles known as the lateral faces. You will learn how to determine the surface area of a trapezoidal prism, as with all three-dimensional shapes.
We know that ,surface area of trapezoid is,
Surface Area= \(\frac{1}{2}\) x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides
In given figure,
∵ value of parallel sides is 10 ft and 13 ft ,
So, the sum of the lengths of the parallel sides= 10+13=23 ft
∵ perpendicular distance between parallel sides= 15 ft
∴ The Surface Area of trapezoid = \(\frac{1}{2}\) x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides
⇒The Surface Area of trapezoid = \(\frac{1}{2}\) x 23 x 15
⇒The Surface Area of trapezoid = \(\frac{1}{2}\) x 345
⇒The Surface Area of trapezoid = 172.5 \(ft^{2}\) ≅ 173 \(ft^{2}\)
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Related Questions
Each hot chocolate at Cocoa Land costs $3.25. Chris has $36.99 to buy chocolate and to pay for a music album to listen to while he studies math. The music album costs $9.99. Which inequality can be used to determine how many hot chocolates, h, Chris can buy?
Answers
Answer:
Step-by-step explanation:
a number decreased by the product of 6 and 3
Answers
Answer:
n-(6*3)
Step-by-step explanation:
a number which is not given so you could use any variable(N).
to decrease means to subtract. the product means multiplication.
so the product of (6*3) decreased from a number (N).
n-(6*3)
example 5.23 in 500 independent calculations a scientist has made 25 errors. if a second scientist checks seven of these calculations randomly, what is the probability that he detects two errors? assume that the second scientist will definitely find the error of a false calculation.
Answers
The probability that a second scientist will detect two errors in seven calculations randomly checked from 500, with a 0.05 error rate, is approximately 4.09%.
This problem can be solved using the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where P(X=k) is the probability of getting k successes (detecting errors), n is the number of trials (7 calculations checked by the second scientist), k is the number of successes (2 errors detected), p is the probability of success in one trial (detecting an error in one calculation), n choose k is the number of ways to choose k successes from n trials, calculated as n! / (k! * (n-k)!).
In this case, n = 7 and k = 2. To find p, we need to know the proportion of errors in the 500 calculations made by the first scientist:
p = number of errors / total number of calculations
p = 25 / 500
p = 0.05
So the probability of detecting two errors in seven calculations checked by the second scientist is:
P(X=2) = (7 choose 2) * 0.05^2 * 0.95^5
P(X=2) = (21) * 0.0025 * 0.7737809375
P(X=2) = 0.0409
Therefore, the probability that the second scientist detects two errors is approximately 0.0409 or 4.09%.
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trucks in a delivery fleet travel a mean of 90 miles per day with a standard deviation of 18 miles per day. the mileage per day is distributed normally. find the probability that a truck drives between 122 and 127 miles in a day. round your answer to four decimal places.
Answers
The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.
To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:
Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ
For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78
For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06
Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803
Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178
So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.
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9. A rectangular shoebox is 14 inches long by 8 inches wide by 6 inches tall.
What is the volume of
the shoebox?
F 28 cubic inches
H 480 cubic inches
G 668 cubic inche
J 672 cubic inches
Answers
Answer:
J 672 cubic inches
Step-by-step explanation:
The volume of a rectangular prism is
V = l*w*h
V = 14 inches * 8 inches * 6 inches
V =672 inches^3
A recipe shows that the yeast needed for a bread recipe is 2 and one-thirdounces. Which of the following decimals is equivalent to this number?2.132.32.ModifyingAbove 3 with bar3.2
Answers
The Answer is B Step-by-step explanation: it's the 2.3 with a line above the 3
let m be the vector space of all 3x3 matrices, and let h be its subspace consisting of all a satisfying. what is the dimension of h
Answers
let m be the vector space of all 3x3 matrices, and let h be its subspace consisting of all a satisfying. The dimension of h will be 0 ≤ h ≤ 3
If m be the vector space , a subset h ⊆ m is a subspace of m if the ten axioms (L₁ , L₂ , L₃ , . . . . L₁₀) of m are satisfied on h but it suffices only two axioms to hold on h for h that are axioms of closure of h under two linear operations : the sum of vectors and their multiplication by scalars in the field F.
Let m is a vector space over a field F, a subset h which is closed under the two linear operation of m : the vector addition and multiplication of vector by scalar .
L₁ (∀x , y ∈m) , x+ y∈ m ---------(1)
L₂ (∀λ ∈ F) ( ∀ x∈ m ) λx ∈m -------(2)
A subset h⊆ m which satisfy (1) and (2) is a subspace of v
Dimension of Vector space and a subspace :
According to linear algebra theorem,
The number of vectors in all the basis if finitely generated vector space m is the same. This number is just the dimension of subspace m : dim m .
If m is spanned then here, dim m = 3
h ⊆ subs m <===> dim h < dim m
If h is subspace of m and dim m = 3 then,
dim h = h with 0≤ h ≤3
If h is zero, the dimension of improper subspace , h = {0}
If dim h = dim m = 3 the h = m since any basis A of h is a basis of m too and conversely,
Hence , any vector m of all 3×3 matrices and h be its subspace , the dim h will be 0 ≤ h ≤ 3
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when would you a subtract in an expression
Answers
Answer:
You would need to subtract when:
Step-by-step explanation:
If there is a negative number like 4 -5
If there is a parentheses,
A subtraction sign.
Hope this helps you.
100 POINTS
PLEASE DO THESE FOUR QUESTIONS (even if it’s just one)
1. write a number sentence expressing the value of the missing angle in the diagram below
2. write a number sentence expressing the value of r in the diagram
3. label the diagram below so that one pair of parallel lines, and one pair of equal lines
4. use the index laws to simplify the expression below, giving your answer with positive indices. SHOW ALL WORKING OUT.
Answers
Step-by-step explanation:
1. k = 76°
2. r = 25cm
3. as the drawing attached
one pair of parallel lines : AB and DC
one pair of equal angles : L A and L D
4. (7²× 3`¹)⁴×7^5 / (3² × 7^(-6))³
= (7^8 × 3`⁴)×7^5/ (3² × 7^(-6))³
= (7^13 × 3`⁴)/ (3^6 × 7^(-18))
= (7^(31) × 3^(-10))
= 7^31 / 3^10
Solve the square of this equation with explanation as I don’t understand please
Answers
===========================================================
Explanation:
Cut the x coefficient (10) in half to get 10/2 = 5. Then square this to get 5^2 = 25.
We'll add 1 to both sides so that the "24" turns into "25", thereby completing the square
x^2 + 10x + 24 = 0
x^2 + 10x + 24+1 = 0+1
x^2 + 10x + 25 = 1
Notice on the left hand side we have something of the form A^2+2AB+B^2 where A = x and B = 5. We can factor this into (A+B)^2, which is the whole reason why we completed the square. You can use the FOIL rule to see how (A+B)^2 expands out into A^2+2AB+B^2. Factoring reverses this process.
This means x^2+10x+25 factors to (x+5)^2 and we now have these steps
(x+5)^2 = 1
x+5 = sqrt(1) or x+5 = -sqrt(1)
x+5 = 1 or x+5 = -1
x = 1-5 or x = -1-5
x = -4 or x = -6 are the two solutions
------------------
Let's check x = -4 to see if it works or not
x^2 + 10x + 24 = 0
(-4)^2 + 10(-4) + 24 = 0
16 - 40 + 24 = 0
-24 + 24 = 0
0 = 0
We get a true equation. That confirms x = -4 is a solution.
If we tried x = -6, then,
x^2 + 10x + 24 = 0
(-6)^2 + 10(-6) + 24 = 0
36 - 60 + 24 = 0
-24 + 24 = 0
0 = 0
That x value is confirmed as well.
Which Line is Perpendicular to y= -1/4x - 8?
A) y=-4x+5
B) y=-1/4x-3
C) y=1/4x
D) y=4x+2
Answers
Answer:
D
Step-by-step explanation:
For two lines to be perpendicular, their gradients must have a product of -1The only one that fits this is DAnswer:
D
Step-by-step explanation:
The product of the slope of the perpendicular lines are -1
y = -1/4x - 8
Slope = -1/4
D) y = 4x + 2
Slope = 4
\(4 * \dfrac{-1}{4}=-1\)
1 individuals in a tetrahybrid cross is AaB-bCcDd. Assuming independent assortment of these four genes, what are the probabilities that F2 offspring will have the following genotypes?
Answers
1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.
2. AABBCcDD: This genotype can be produced in two ways:
a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.
The probability of this happening is = 1/128.
b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.
3. The probability of this happening is 1/32.
AaBbCcDd : The probability of this happening is 1/256.
4. aaBBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is 1/128.
b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is 1/32.
To solve this problem, we need to use the principles of probability and Punnett squares.
For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.
Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:
A | A | a | a
---|-----|-----|----
B | B | b | b
---|-----|-----|----
C | C | c | c
---|-----|-----|----
D | D | d | d
Each box in the Punnett square represents a possible combination of alleles from the two parents.
For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.
We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.
AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.
The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.
AABBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.
The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)
b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)
AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).
The probability of this happening is \((1/2)^8 = 1/256.\)
aaBBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)
b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)
Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.
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evaluate the data in the figure below. what aspects of the data are researchers likely to be confident about? what aspects of the data are more likely to change as more data are collected?
Answers
Aspects of the data that are more likely to change as more data are collected include inconsistent trends, small sample sizes, and the presence of outliers.
1. Aspects researchers are likely to be confident about:
Consistent trends: If there is a clear, consistent trend in the data, researchers may have more confidence in these aspects.
Large sample size: When the data is based on a large number of observations, researchers may have greater confidence in the results.
Statistical significance: If the results show statistically significant differences or correlations, this can increase the researchers' confidence in the data.
2. Aspects that are more likely to change as more data are collected:
Inconsistent trends: If the data shows fluctuating trends, more data collection may lead to changes in the interpretation of the data.
Small sample size: When the data is based on a small number of observations, the results may not be as reliable and can change as more data is collected.
Outliers: Outliers can greatly affect the interpretation of the data, but as more data is collected, their impact may be reduced, and the overall understanding of the data can change.
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For 2, use the relationship between the values of the digits to solve Write a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864
Answers
Answer:
New Digit = 315,864
Step-by-step explanation:
Given:
Digit - 135,864
Value of digit 3 = 30,000
Find:
New Digit, Value of 3 is 10 times greater
Computation:
Value of 3 is 10 times greater = (30,000) = 300,000
New Digit = 315,864
15. Rob wants to purchase a $5,000 drum set. The music store offers him a
2-year installment agreement requiring $800 down and monthly payments of
$202.50. Rob has a poor credit rating.
c. How much interest would the finance company charge?
d. Should Rob use the installment plan or borrow the money from the finance
comman??
Answers
Answer:
Step-by-step explanation:
c. $395 in interest rate
d. Rob should use the installment plan
Which verbal expression best describes the algebraic expression 2x ÷ 4? (4 points) Group of answer choices The quotient of two and some number times four The sum of two and some number divided by four The quotient of two times some number and four The product of some number and four divided by two
Answers
Answer:
C. The quotient of two times some number and four
Step-by-step explanation:
Given the expression 2x÷4
The x be the unknown number.
2x can be written as:
Product of some number and 2 OR two times an unknown number
2x÷4 will then be written as:
The quotient of two times a number and 4
The correct option to describe the equation is "The quotient of two times some number and four"
t is known that a batch of toys produced at a certain factory in a day has a defect rate of 1%. suppose the quality inspectors randomly inspect 500 toys from the batch and calculate the proportion of defective toys, what will the the sampling distribution look like? the sampling distribution would be centered around , with a standard deviation of .
Answers
Therefore, the sampling distribution will be centered around 0.01, with a standard deviation of 0.0098.
What will the the sampling distribution look like?In a random sample of 500 toys from the manufacturer batch, the fraction of defective toys will have a sampling distribution that is roughly normal.
The population proportion of defective toys will be used as the sampling distribution's mean, which is 1% or 0.01. This is thus because a proportion of the sample is a fair estimate of a proportion of the population.
The following formula can be used to determine the standard error, also known as the standard deviation, of the sample distribution:
SE is equal to sqrt[(p*(1-p))/n]
where n is the sample size, 500, and p is the population proportion of faulty toys, which is 0.01.
These values are substituted into the formula to produce:
SE is equal to sqrt[(0.01*(1-0.01))/500] = 0.0098
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solve the inequalities show each solution as an interval on the number line 41-x<17
Answers
The inequality in the expression 41-x < 17 is the less than inequality
The solution to the inequality is x > 24
How to solve the inequality?The inequality is given as:
41-x < 17
Subtract 41 from both sides of the inequality
41 - 41 -x < 17 - 41
Evaluate the difference
-x < -24
Multiply both sides by -1
-1 * -x < -24 * -1
Evaluate the product
x > 24
Hence, the solution to the inequality is x > 24
See attachment for the number line
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PLEASE HELP ME ASAP!!!!!
Answers
Answer:
First off lets note that this is an iscocleles triangle since the 2 base angles are equal. Additionally, we know that the 2 sides adjacent to the base are equal in iscocleles triangles. Therefore, RP=RQ
With that in mind, lets solve:
If RP=RQ then we can make the equation \(5x-4 = x+4\) by using substitution
Now, we can solve for x:
\(5x-4 = x+4\)
\(5x-x-4=x-x+4\)
\(4x-4 = 4\)
\(4x-4+4 = 4+4\)
\(4x = 8\)
\(4x/4=8/4\)
\(x=2\)
Now that we know what x is equal to we can solve for PR
\(PR = 5(2)-4\)
\(PR = 10-4\)
\(PR = 6\)
Hope this helped!
Step-by-step explanation:
What is the y intercept of this graph?. What is the slope?
Answers
Answer:
y intercept is -3
slope is 4
y=4x-3
Step-by-step explanation:
Consider the following set of numbers:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
What is the probability of drawing an odd number or a
multiple of 3?
Answers
Answer:
Probability of drawing an odd number.
Number of odd numbers = 5
Number of numbers in the set = 10
So it's a 5 in 10 chance or 1 in 2 chance.
Probability of drawing a multiple of 3.
Multiples of 3 in the set = 3, 6 and 9 = 3 multiples of 3
Number of numbers in the set = 10
So it's a 3 in 10 chance
hideo is calculating the standard deviation of a data set that has 7 values. he determines that the sum of the squared deviations is 103. what is the standard deviation of the data set?
Answers
Therefore, the standard deviation of the data set is approximately 4.14.
The standard deviation is calculated by taking the square root of the variance, which is the sum of the squared deviations divided by the sample size minus 1.
So, first we need to calculate the variance:
variance = sum of squared deviations / (sample size - 1)
variance = 103 / (7 - 1)
variance = 17.17
Now we can find the standard deviation:
standard deviation = √(variance)
standard deviation = √(17.17)
standard deviation = 4.14 (rounded to two decimal places)
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What is the THEORETICAL probability of choosing a vowel?
Based on the experiment, what is the probability of choosing a vowel?
Answers
The THEORETICAL probability of choosing a vowel is 3/8 and the experimental probability is 36/75
What is the probability of choosing a vowel?From the question, we have the following parameters that can be used in our computation:
Vowels = Letters A, I and EVowels = Letters of the word SAPPHIREIn the letters of the word, we have
Vowels = 3
Letters = 8
By calculation, the theoretical probability of choosing a vowel is
Theoretical probability = Vowels/Letters
So, we have
Theoretical probability = 3/8
Based on the experiment, we have
Vowels = 15+9+12 = 36
Letters = 8+15+7+5+20+20 = 75
So, we have
Experimental probability = 36/75
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Four-fifths the sum of twice a number and nine is equal to negative
twenty-eight. What is the number?
Answers
Answer:
The number should be -22
Step-by-step explanation:
4/5(2x + 9) = -28
2x + 9 = - 35
2x = - 44
X = -22
the sum of twice a number, x, and 6 is equal to 4 more than the number, x. what is the vaule of x.
Answers
Answer:
2x+6=x+4
2x-x = 4-6
x= -2
Answer:
x=-2
Step-by-step explanation:
cuz , if u added them together the sum would be -2+6=4 , is that ur question? or I've answered smth that has nothing to do?
please help marking brainlist
Answers
Answer:
7/10
Step-by-step explanation:
Try 7/10
(7/10)^2=49/100
Una casa fue comprada en 1990 en 1,200,000. 00 y en 2005 fue vendida
Answers
The conversion of the purchase and sale amounts to English would be as follows: 1,200,000.00 in 1990 and the sale amount in 2005. In 1990, a house was bought for 1,200,000.00.
The amount mentioned is not specified in a particular currency, so we'll assume it is in US dollars. The house was then sold in 2005. Since the conversion rates may vary depending on the specific dates and exchange rates, the actual equivalent amounts in English currency would need to be determined using the appropriate historical data for 1990 and 2005.
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QUESTION: A house was purchased in 1990 for 1,200,000.00, and was sold in 2005.
Determine a series of transformations that would map figure F onto figure G.
PLEASE ASAP
Answers
Answer:
reflection, translation
Step-by-step explanation:
I can explain it if you want if you reply to this but since you are in a hurry that'll take too long to type right now haha
What is the Sin(B)? Need help!
Answers
Answer:
Last option: 5/8
Step-by-step explanation:
sin(angle) = opposite / hypotenuse
So, sin(B) = 4/6.4 = 20/32 = 10/16 = 5/8
Hope this helps!
Solve the system of equations using substitution or elimination:
x = 3y + 6
2x - 4y = 8
Answers
Answer:
x=0, y=-2
Step-by-step explanation:
Let x=3y+6 be equation 1
and 2x-4y=8 be equation 2
sub equation 1 into equation2,
2(3y+6)-4y=8
6y+12-4y=8
2y=-4
y=-2
sub y=-2 into equation 1,
x=3(-2)+6
x=0
sub is an abbreviation for substitute