Answer:
We can use the Pythagorean theorem to find the distance between the transmitter and the second city:
c² = a² + b²
c² = 55² + 51²
c² = 3026
c ≈ 55.01
So the transmitter is about 55.01 miles away from the second city.
To determine how much of the drive will pick up a signal, we can draw a circle with a radius of 40 miles centered at the transmitter, and see which part of the line connecting the two cities is within this circle.
We can see that the line connecting the two cities intersects the circle at two points, forming a right triangle with one leg measuring 40 miles. We can use trigonometry to find the length of the other leg:
sin(theta) = opposite/hypotenuse
sin(theta) = 40/c
csin(theta) = 40
a = csin(theta)
a = 55.01*sin(theta)
Now we need to find the angle theta, which can be found using inverse tangent:
tan(theta) = opposite/adjacent
tan(theta) = 55/51
theta = tan⁻¹(55/51)
theta ≈ 49.72 degrees
So we can substitute this value of theta into the equation we found earlier for a:
a ≈ 43.89
Therefore, the length of the line segment within the circle is approximately 43.89 miles. To find the length of the entire line segment connecting the two cities, we can use the Pythagorean theorem again:
b² = c² - a²
b² = 55.01² - 43.89²
b ≈ 33.6
So the entire length of the line segment connecting the two cities is approximately 33.6 miles. Therefore, the portion of the drive during which you will pick up a signal from the transmitter is 43.89/33.6 = 1.31 hours or about 79 minutes.
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?
1. AABBCCDD: The probability of this happening is [tex]1/16[/tex], 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 [tex](1/2)^4 = 1/16[/tex] , 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[tex](1/2)^4 * 1/2 * (1/2)^3 = 1/128[/tex]
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[tex]2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32[/tex]
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 [tex](1/2)^8 = 1/256.[/tex]
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[tex](1/2)^4 * 1/2 * (1/2)^3 = 1/128.[/tex]
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 [tex]2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.[/tex]
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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In regression and correlation analysis, if SSE and SST are known, then with this information the
A) coefficient of determination can be computed
B) slope of the line can be computed
C) Y intercept can be computed
D) x intercept can be computed
A) The coefficient of determination can be computed using the SSE and SST values in regression and correlation analysis.
SSE (Sum of Squared Errors) is the sum of the squared differences between the actual and predicted values of the dependent variable. SST (Total Sum of Squares) is the sum of the squared differences between the actual values of the dependent variable and their mean.
The coefficient of determination, denoted as R², measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model.
It is calculated as follows:
R² = 1 - (SSE/SST)
Since both SSE and SST are given, you can compute the coefficient of determination.
However, the information provided is not sufficient to calculate the slope, Y-intercept, or X-intercept of the regression line.
Based on the given information, the correct answer is:
A) Coefficient of determination can be computed.
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This coefficient of determination (R²) gives you a measure of how well the regression line fits the data in your correlation analysis.
A) The coefficient of determination can be computed with the known values of SSE (sum of squared errors) and SST (total sum of squares) in regression and correlation analysis. The coefficient of determination is a measure of how well the regression line fits the data and is expressed as a percentage. It represents the proportion of variability in the dependent variable (Y) that can be explained by the independent variable (X).
Based on the information provided, with the known SSE (Sum of Squares Error) and SST (Sum of Squares Total), you can compute the coefficient of determination. So, the correct answer is:
A) Coefficient of determination can be computed
To calculate the coefficient of determination (R²), follow these steps:
1. Calculate the Sum of Squares Regression (SSR) by subtracting SSE from SST:
SSR = SST - SSE
2. Compute the coefficient of determination (R²) by dividing SSR by SST:
R² = SSR / SST
This coefficient of determination (R²) gives you a measure of how well the regression line fits the data in your correlation analysis.
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Which property is shown in the following statement?
3 + (-6) = -6 + 3
Answer:
The mathematical property demonstrated by the statement 3 + (-6) = -6 + 3 is the commutative property of addition.
This states that: A + B = B + A
The commutative property of addition is the property that is demonstrated by the formula "3 + (-6) = -6 + 3".
This characteristic states that the sum is unaffected by the sequence in which two numbers are added. In other words, a + b = b + a for any two numbers a and b.
In this instance, the left side has 3 + (-6) which equals -3. We have -6 + 3 on the right side, which also equals -3. This indicates that the result is unaffected by the sequence in which the numbers are added.
We can thus write:
3 + (-6) = -6 + 3
-3 = -3
This demonstrates the truth of the assertion and serves as an illustration of the commutative property of addition.
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A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The percentage of people who said they preferred Candidate A was 80%. The margin of error for the survey was 4%. Which of the following is not a reasonable value for the actual percentage of the population that prefers Candidate A? Group of answer choices 75.6% 82.4% 76.4% 83.3%
83.3% is outside the range and therefore not a reasonable value.
How to determine which value is not a reasonable value?
We need to take into account the margin of error in order to determine which value is not a reasonable one for the actual proportion of the population that favors Candidate A. The range within which the actual population value is likely to fall is shown by the margin of error.
We can determine the likely range of the true population value as follows if the sample contained 80% of those who preferred Candidate A and the margin of error was 4%:
The lower bound of the range is 80% - 4% = 76%
The upper bound of the range is 80% + 4% = 84%
Therefore, any value outside of this range is not a reasonable value for the actual percentage of the population that prefers Candidate A.
75.6% is within the range and therefore a reasonable value.
82.4% is within the range and therefore a reasonable value.
76.4% is within the range and therefore a reasonable value.
83.3% is outside the range and therefore not a reasonable value.
So the answer is 83.3%.
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URGENT! Will give brainliest
The formula =C6*D6 would be found in which cell of this spreadsheet?
A. E6
B. E3
C.D3
D. B6
Answer:A. E6
Step-by-step explanation: Just did it :)
solve this. and you will get brainlst.
Step-by-step explanation:
Tan 20 = 50 / d
d = 50 / tan 20 = 137 m
The simplified slope of item number 2 is:
a. 1/6
b. 6
c. -6
d. -1/6
The simplified slope of item number 3 is:
a. 4/7
b. 3/4
c. 7/4
d. -4/3
The simplified slope of item number 4 is:
a. 3/5
b. -3/5
c. -5/12
d. -12/5
Answer:
c and a
Step-by-step explanation:
Questions 4, 5, and 6 on 8-3 geometry quiz. Attachment included: please help and show your work
The requried solution to the given trigonometric problems area shown below,
4. G 30 foot, 5. C 40 and 6. F 20.5.
4.
Let,
x = length of ramp = 14 ft
n = base of the ramp
the angle of inclination of the ramp with the base is Ф=22.2°,
The base of the ramp is given by trigonometric ratios,
cosФ = n/x
cos22.2 = b / 14
b = 13 foot
Similarly,
5. c. 40
6. F 20.5
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Which is colder 32F or -109F
Answer:
Step-by-step explanation:
-109f
Que tanto mas alto era la calificacion mas alta del examen que la calificacion mas baja
As per the fraction, the lowest score in the examination is 44.
Let's consider the given information. We are told that the highest score and the lowest score in an examination differ by 55 marks. We can represent the highest score as x and the lowest score as y. Therefore, we have:
x - y = 55 ----- equation 1
We are also given that the higher score, which is x, is 9/4 times the lower score, which is y. This can be represented as:
x = (9/4)y
We can use this equation to substitute x in equation 1 and solve for y.
Substituting x in equation 1, we get:
(9/4)y - y = 55
Simplifying the above equation, we get:
(5/4)y = 55
Multiplying both sides by 4/5, we get:
y = 44
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Complete Question:
In an examination, the highest score and the lowest score are different by 55 and the higher one was 9/4 times the lower one. Find the lowest score.
If 68 colored pencils are split evenly between 4 students, how many pencils does each student get?
Each person will get 17 pencils.
What is Division?
Division is the opposite of multiplication. For example, If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division.
The main goal of dividing is to see how many equal groups are formed or how many are in each group when sharing fairly.
In the problem given above, to divide 68 colored pencils to 4 students each, you will have to put 68 colored pencils for each student. So, 68 divided by 4 will give the result 17.
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Answer is D.
Can anyone explain why??
The true statement regarding the hypothesis will be:
II. A 95 percent confidence interval for the difference in means will contain the value 0.III. A 99 percent confidence interval for the difference in means will contain the value 0.The correct option is D II and III only.
How to explain the hypothesisA two-sample t-test of the hypotheses Hoμ1-2 = 0 versus H 41-μ2> 0 produces a p-value of 0.03.
In this case, a 95 percent confidence interval for the difference in means will contain the value 0.
Also, a 99 percent confidence interval for the difference in means will contain the value 0.
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Jenny is building a kite, as show below.one of the crossbars is 50 1/2cm long and the other is 90 1/2 cm long,how much fabric does she need?
The amount of fabric that should be used to build a kite with the above given dimensions would be = 2,285.125cm²
How to calculate the area of a kite?To calculate the area of a kite the formula that should be used would be = 1/2 d1d2
where d1 = 50½cm
d2 = 90½cm
The area of the kite;
= 1/2 × 50.5×90.5b
= 4570.25/2
= 2,285.125cm²
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A farmer is planning to create a new grazing field for
his horses. He determines that he needs 280 yards of fencing
for his new field. The fencing is sold by the foot. How many
feet of fencing should the farmer buy? Explain.
Answer:
840 feet
Step-by-step explanation:
1 yard = 3 feet
280 yards = x
x = 280 × 3
x = 840 feet
Rewrite 4.86 x 104 in decimal notation.
O48,600
O4, 860,000
O 0.000486
O 4.86
If we rewrite 4.86 x 104 in decimal notation, we will have 48,600. The Option A.
What is the decimal notation of 4.86 x 104?In decimal notation, 4.86 x 104 is equivalent to 48600. To convert scientific notation to decimal notation, you simply move the decimal point to the right by the number of places indicated by the exponent.
In this case, since the exponent is 4, you move the decimal point four places to the right of the digit 4, resulting in 48600. Therefore, 4.86 x 104 in decimal notation is 48600.
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this is tomorrow pls help
For the heights, areas and perimeters of the shapes:
5. the trapezoid has a height of 10.4 cm.6. area of the equilateral triangle is 97.31 square inches.7. the size of the inscribed square is 84.5 in².8. the rhombus's side length is 6 inches.How to find area, perimeter and height?5. The trapezoid can be divided into a rectangle and a right triangle. Let the height of the trapezoid be h.
The area of the trapezoid is A = (1/2)(13.9 + 9.3)h = 11.6h.
We are given that A = 120.8cm², so solve for h:
11.6h = 120.8
h = 10.4 cm
Therefore, the height of the trapezoid is 10.4 cm.
6. Let s be the side length of the equilateral triangle. Then, we have:
s + s + s = 45
3s = 45
s = 15
The perimeter of the equilateral triangle is 45 inches.
The area of an equilateral triangle can be found using the formula:
Area = (√(3)/4)s²
Plugging in s = 15:
Area = (√(3)/4)(15²) = 97.31 in²
Therefore, the area of the equilateral triangle is 97.31 square inches.
7. Let a be the side length of the inscribed square and let A be the area of the inscribed square. Let b be the side length of the circumscribed square.
The area of the outer square is 169in², so b² = 169. Therefore, b = 13.
The diagonal of the inscribed square is equal to the diameter of the circle, which is equal to the side length of the outer square. Therefore, a×√(2) = 13.
Solving for a:
a = 13/√(2) = 9.19
The area of the inscribed square is A = a² = (13/√(2))² = 84.5 in².
The ratio of the area of the inscribed square to the area of the circumscribed square is:
A/(b²) = 84.5/169 = 0.5
Therefore, the area of the inscribed square is half the area of the circumscribed square.
8. Let d₁ and d₂ be the diagonals of the rhombus. Let s be the side length of the rhombus.
We know that d₁ = 6 inches and d₂ = 8 inches. We also know that the diagonals of a rhombus intersect at a right angle and bisect each other. Therefore, we can form a right triangle with legs of length s/2 and s/2 and hypotenuse of length d₁/2.
Using the Pythagorean theorem:
(s/2)² + (s/2)² = (d1/2)²
s²/4 = 9
s = 6
Therefore, the side length of the rhombus is 6 inches.
The perimeter of the rhombus is 4s = 24 inches.
The area of the rhombus can be found using the formula:
Area = (1/2)d₁d₂
Plugging in d₁ = 6 and d₂ = 8:
Area = (1/2)(6)(8) = 24 square inches
Therefore, the perimeter of the rhombus is 24 inches and the area of the rhombus is 24 square inches.
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On the way to her babysitting job, Mary rode her bike for the first mile. She stopped at a traffic light and waited a few minutes for the traffic light to turn green. She then walked her bike across the street and up a short steep hill. Finally, she rode the bike at a constant speed for one more mile. If Mary created a graph of her time and distance, which statement describes the part of her graph that would show no change in distance?
Mary used her bike to ride the first mile.
Mary stopped and waited for the traffic light to turn green.
Mary walked her bike across the avenue and up a short hill.
Mary rode her bike at a constant speed for one mile.
The part of the graph that would show no change in distance is when Mary stopped and waited for the traffic light to turn green.
Statement B is correct.
How do we calculate?We know that during this time, Mary did not move forward or cover any distance. Hence, the graph would show a flat line at this point, indicating no change in distance.
Distance is described as a numerical or occasionally qualitative measurement of how far apart objects or points are.
In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
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Kimble is trying to decide between two checking account plans. Plan A offers a quarterly compound interest rate of 0.5%, while plan b offers a 3.5% interest compound annually. Which is the better plan? By how much?
Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975% in the compound interest.
What is compound interest?When interest is earned on a loan or investment, it is earned on both the principal and any accumulated interest, which is known as compound interest. In other words, interest is added to the principal, and the resulting sum is then used to determine future interest. Compounding causes an investment or loan to increase more quickly than it would with simple interest, where just the principal is charged interest. Compounding may occur daily, monthly, quarterly, annually, or at any other interval.
To compare the plans of the two accounts we have:
Rate = ( 1 + rate / n)ⁿ - 1
where, n is the compounded period.
For plan A:
Effective annual interest rate = (1 + (0.5%/4))⁴ - 1 ≈ 0.5025%
For Plan B, we have:
Effective annual interest rate = (1 + 3.5%)¹- 1 = 3.5%
Comparing the two we see that Plan B offers higher rates by:
3.5% - 0.5025% ≈ 2.9975%.
Hence, Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975%.
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if sally gets scores 73, 85, 93, the 4th score is 20 points less than 5th score which is 2/3 of the average of the first three. what must she score on the 6th and 7th test to average an 85
There is no solution that allows Sally to average an 85 with the given scores.
Let's start by finding the 5th score:
We know that the 4th score is 20 points less than the 5th score, so let's call the 5th score "x". Therefore, the 4th score is "x - 20".
We also know that the 5th score is 2/3 of the average of the first three scores. The average of the first three scores is (73 + 85 + 93)/3 = 83.67. So, (2/3) * 83.67 = 55.78 is the 5th score (rounded to two decimal places).
Therefore, x = 55.78/(2/3) = 83.67 is the 5th score.
Now, let's calculate the total score Sally needs to average an 85:
She already has 73 + 85 + 93 + 83.67 = 334.67 points. To average an 85 over seven tests, she needs a total of 7 * 85 = 595 points.
To find the scores she needs on the 6th and 7th tests, we can subtract the points she already has from the total points she needs:
595 - 334.67 = 260.33
So, Sally needs a total of 260.33 points on the 6th and 7th tests combined.
Let's call the 6th score "y" and the 7th score "z". We can set up an equation to solve for these two scores:
(y + z)/2 = 260.33
Multiplying both sides by 2:
y + z = 520.67
Since Sally needs to average an 85 over seven tests, the sum of all seven scores must be:
7 * 85 = 595
The sum of the first five scores is:
73 + 85 + 93 + 83.67 + 83.67 = 418.34
So, the sum of the last two scores must be:
595 - 418.34 = 176.66
Now we can set up another equation:
y + z = 176.66
We can solve this equation for one of the variables. Let's solve for "y":
y = 176.66 - z
Now we can substitute this into the first equation:
(176.66 - z + z)/2 = 260.33
176.66/2 = 260.33
88.33 = 260.33
This equation does not make sense.
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(6 + 7) - 1 = (5 × 2) + ___ which numbers belong to make this sentence true
a company advertises that food preparation time can be significantly reduced with the handy dandy slicer. a sample of 12 individuals prepared the ingredients for a meal with and without the slicer. you are given the preparation times below. preparation times person with slicer without slicer 1 20 22 2 12 18 3 20 18 4 14 22 5 19 19 6 20 21 7 19 18 8 15 12 9 22 18 10 19 25 11 21 26 12 23 20 the null hypothesis should . a. be revised b. not be rejected c. be rejected
For the food preparation time data with or without slicer, the null hypothesis for this sample data should not be rejected. So, option (b) is right answer.
We have a food preparation time data of a company. The time of preparation is significantly reduced with the handy dandy slicer. Sample size, n = 12
We have a table present in above figure which has the preparation times data consists people, with slicer and without slicer. First we calculate difference between with slicer and without slicer data, that d: -2, -6, 2, -8 , 0, -1, 1, 3, 4, -6, -5, 3.
We do all work on the difference, d.
Mean value of difference d, [tex]\bar d = \frac{\sum_{i = 1}^{n} {d_i }}{n}[/tex] = -1.25
Standard deviations, [tex] \sigma = \sqrt{\frac{ \sum {d_i^2 - (\sum d_i)²}}{n - 1}}
[/tex] = 4.115
degree of freedom= 12 - 1 = 11
Let level of significance = 0.05
The null and alternative hypothesis are defined as [tex]H_0 : \mu_d = 0 [/tex]
[tex]H_a: \mu_d < 0[/tex]
Using t-test, [tex]t = \frac{ \bar d} {\frac{ \sigma}{ \sqrt{n}}}[/tex]
[tex]= \frac{ -1.25} {\frac{ 4.115}{ √12}}[/tex]
= - 1.05
Now, using t-distribution table, value of p for t = -1.05 for 11 degree of freedom is -1.796. So, p-value = -1.796 < 0.005, Hence, we should not reject the null hypothesis.
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HELP I NEED HELP PLEASE THANKS I HAVE SCHOOL IN 30 MINUTES PLEASE
Answer:
5. 1 line
6. none
7. 2 lines
8. 1 line
9. 1 line
25. f(x) =
x + 4
x-3
The x-intercept is (-4, 0). The y-intercept can also be located by setting x = 0: f(0) = (0 + 4)/(0 - 3) = -4/3. So the y-intercept is (0, -4/3).
The f x formula, what is it?By rearranging the equation to take on its general form, f(x) = mx + c, where m is the slope, one can determine the slope of a linear function. By rearranging the equation to take on its general form, the vertex of a quadratic function can be determined.
The formula for f(x) is
f(x) = (x + 4)/(x - 3)
This function is rational, which means it is the ratio of two polynomials. X + 4 makes up the numerator, and X – 3 makes up the denominator.
Several things about this function are worth mentioning:
Due to the illogical nature of division by zero, the denominator cannot be equal to zero. As a result, at x = 3, there is a vertical asymptote and the function is undefined.
The function cannot be further simplified because the numerator and denominator have no shared factors.
The function approaches the horizontal asymptote y = 1 when x approaches positive or negative infinity because the maximum power of x in the numerator and denominator is the same (both are 1).
To graph this function, we can start by plotting the vertical asymptote at x = 3, and the horizontal asymptote at y = 1. The x-intercept can alternatively be determined by setting the numerator to zero:
x + 4 = 0
x = -4
So the x-intercept is (-4, 0).
f(0) = (0 + 4)/(0 - 3) = -4/3
So the y-intercept is (0, -4/3).
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Please help me this would bring my grade up ALOT!
THANK YOU SO MUCH !!!!!!!!!!!!!!!!!!!!
Answer:
To determine the number of sheets of cardboard in a stack, we need to use the information given in the problem.
We know that each sheet of cardboard is 1 inch thick, and 16 sheets are stacked on top of each other in packages. The height of each stack is 21 inches.
Using the model of a ruler, we can divide the height of the stack (21 inches) by the thickness of each sheet (1 inch) to find the number of sheets in the stack.
21 ÷ 1 = 21
So, there are 21 sheets of cardboard in a stack.
To write an expression that can be used to determine the number of sheets of cardboard in a stack, we can use:
Number of sheets = height of stack ÷ thickness of each sheet
Or, substituting the given values: Number of sheets = 21 ÷ 1 = 21
This expression is simply a representation of the model we used earlier. It shows that we can determine the number of sheets in a stack by dividing the height of the stack by the thickness of each sheet. In this case, the expression yields the same result as the model, which is 21 sheets.
helicopters The four blades of a helicopter meet at right angles and are
all the same length. The distance between the tips of two adjacent blades
is 36 ft. How long is each blade? Round your answer to the nearest tenth.
Can you pls help? This is geometry
The equation of the circle with center (3, -4) and a radius of 6 units is (x - 3)^2 + (y + 4)^2 = 36.
How to explain the equationThe equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values given, we get:
(x - 3)^2 + (y + 4)^2 = 6^2
Expanding and simplifying, we get the final equation of the circle:
(x - 3)^2 + (y + 4)^2 = 36
Therefore, the equation of the circle with center (3, -4) and a radius of 6 units is (x - 3)^2 + (y + 4)^2 = 36.
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Im stuck on this question
An image of a right rectangular prism is shown. A rectangular prism with dimensions of 4.5 centimeters by 6 centimeters by 4 centimeters. What is the surface area of the prism? 138 cm2 169 cm2 31 cm2 69 cm2
The prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.
What is the meaning of surface area?A three-dimensional object's surface area is the sum of all its faces.
The formula for the surface area of a right rectangular prism is:
surface area = 2lw + 2lh + 2wh
where l, w, and h are the prism's length, breadth, and height, respectively.
When we substitute the provided values, we get:
Surface Area = 2(4.5)(6) + 2(4.5)(4) + 2(6)(4)
Surface Area = 54 + 36 + 48
surface area = 138 [tex]cm^{2}[/tex]
As a result, the prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.
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Collina’s Italian Café in Houston, Texas, advertises that carryout orders take about 25 minutes (Collina’s website, February 27, 2008). Assume that the time required for a carryout order to be ready for customer pickup has an exponential distribution with a mean of 25 minutes.a. What is the probability than a carryout order will be ready within 20 minutes?b. If a customer arrives 30 minutes after placing an order, what is the probability that the order will not be ready?c. A particular customer lives 15 minutes from Collina’s Italian Café. If the customer places a telephone order at 5:20 P.M., what is the probability that the customer can drive to the café, pick up the order, and return home by 6:00 P.M.?
The probability of a carryout order being ready within 20 minutes is approximately 0.5507
We know that the time required for a carryout order to be ready for customer pickup follows an exponential distribution with a mean of 25 minutes. The probability density function for an exponential distribution is given by
f(x) = λe^(-λx)
where λ is the rate parameter
We can find the rate parameter λ using the mean
mean = 1/λ
λ = 1/mean = 1/25 = 0.04
So the probability of a carryout order being ready within 20 minutes is
P(X ≤ 20) = ∫₀²⁰ λe^(-λx) dx
P(X ≤ 20) = [-e^(-λx)]₀²⁰
P(X ≤ 20) = [-e^(-0.04x)]₀²⁰
P(X ≤ 20) = [-e^(-0.8)] - [-1]
P(X ≤ 20) = 0.5507
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The given question is incomplete, the complete question is:
Collina’s Italian Café in Houston, Texas, advertises that carryout orders take about 25 minutes (Collina’s website, February 27, 2008). Assume that the time required for a carryout order to be ready for customer pickup has an exponential distribution with a mean of 25 minutes. What is the probability than a carryout order will be ready within 20 minutes?
Ms. Barnett is packing orders for her soap business. One customer ordered 12 bars of her Orange You Fresh soap. If each bar of soap weighs 4 ounces, how many pounds will this order weigh?
Using mathematical operations of division and multiplication, the total weight of the order in pounds is 3 pounds.
How the total weight is computed?The total weight is firstly computed in ounces before being converted into pounds.
The computation follows the mathematical operations of multiplication and division, respectively.
The number of Orange You Fresh soap bars ordered by a customer = 12
The weight of each bar of soap = 4 ounces
The total weight of 12 bars in ounces = 48 ounces (4 x 12)
1 pound = 16 ounces
3 pounds = 48 ounces (48 ÷ 16)
Thus, based on mathematical operations, the number of pounds this order will weigh is 3 pounds.
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i need help please help me
You can take a look at this, the image that I attached might help.
For example, the first one shifts left because the h value is positive 3. -(3) = -3.