Answer:
dimensions: 12 ft by 5 ftarea: 60 ft²Step-by-step explanation:
Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...
x² + (x+7)² = 13²
2x² +14x + 49 = 169 . . . . eliminate parentheses
x² +7x -60 = 0 . . . . . subtract 169 and divide by 2
(x +12)(x -5) = 0 . . . . factor the equation
x = -12 or +5 . . . . . . . only the positive value of x is useful here.
The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².
_____
Comment on finding the area
The quadratic equation above can be rearranged and factored as ...
x(x +7) = 60
Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.
To the nearest tenth the value of x that satisfies 2x = −2x + 11 is
Answer:
2.8 (from 2.75 because of rounding)
Step-by-step explanation:
2x = -2x + 11
Add 2x on both sides
4x = 11
Divide 4 on both sides
x = 11/4
x = 2.75
Round to nearest tenth
x is about 2.8
Please mark me for brainliest :D !! Thanks!
Answer:
x = 2.8
Step-by-step explanation:
2x = - 2x + 11 Add 2x to both sides.
2x+2x = -2x+2x + 11 Combine
4x = 11 Divide by 4
4x/4 = 11/4
x = 2 3/4
x = 2.75
Rounded to the 10th place, you would get 2.8
In order to avoid a training violation, 85% of your store's employees must complete diversity training by the end of the week. You have 142 employees at your store and 91 have currently completed the training. How many more employees must complete the training by the end of the week to avoid a training violation? 15 20 25 30 45
Multiply the number of total employees by 85%:
142 x 0.85 = 120.7, round to 121
121 total people need to complete the training.
Now subtract the number of people who already took the training:
121 - 91 = 20
20 more people need to take it.
A coin is tossed and a single die is rolled. What is the probability that the coin shows heads and the die shows a 3 or a 4?
Answer:
1/6
Step-by-step explanation:
landing on heads is a 1/2% and landing on a 3 or 4 is a 1/3 then multiply together
sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie having been eaten before she can put the topping on. how much 1 square inch strips of dough will she need for the top, now that a portion is missing? round your answer to the nearest while nimber.
Answer:
131
Step-by-step explanation:
We need to find the area of the top of the pie that is leftover. To do this, we use the formula for the area of a circle and multiply by 0.65 since that is how much of the pie is left.
A = 0.65π[tex]r^{2}[/tex] = 0.65π[tex]8^{2}[/tex] = 130.69025 [tex]in^{2}[/tex]
If each strip of dough is 1 square inch, the total strips of dough needed is 131.
The total strips of dough needed is 131 if Sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
Sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie having been eaten before she can put the topping on.
Area of circle:
A = 0.65πr² = 0.65π(8)²
A = 130.69025 square inches ≈ 131 square inches
If each strip of dough is 1 square inch
The total strips of dough needed = 131/1 = 131
Thus, the total strips of dough needed is 131 if Sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie.
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Five friends are going to the theater. They have purchased a row of five seats with an aisle on either end. James doesn't want to sit next to Jill Betty and Herb are dating and want to sit next to each other Bob must sit on an aisle Provide a seating order that conforms to the above rules. An example of an invalid seating order is: James, Betty, Herb, Bob, Jill The above arrangement is invalid because: Bob is not sitting on an aisle. Specify the seating order as the names separated by s (as in the above example). Please be sure to spell the names correctly, including capitalization.
Answer:
Bob, Jill, Betty, Herb, James
Final answer:
A valid seating arrangement for the five friends is either Bob, Betty, Herb, James, Jill, or Jill, James, Herb, Betty, Bob. Each arrangement adheres to all given conditions: Bob is on an aisle, Betty and Herb are seated together, and James is not sitting next to Jill.
Explanation:
To solve the seating problem for the five friends going to the theater, we must adhere to the conditions: Bob must sit on an aisle, James cannot sit next to Jill, and Betty and Herb want to sit next to each other. Bearing in mind that there's an aisle on either side of the row of five seats, we can begin by placing Bob on an aisle seat since he must sit on one. This can either be the first seat on the left or the right. Since James doesn't want to sit next to Jill, we can't place Jill next to Bob if we sit James on the other end to maximize distance between them. Betty and Herb must sit together, which can only happen in the three seats left in the middle.
Here is a seating arrangement that satisfies all conditions: Bob, Betty, Herb, James, Jill. In this arrangement, Bob is on an aisle, Betty and Herb are seated together, and James is not sitting next to Jill.
Alternatively, if we place Bob on the other aisle, we get: Jill, James, Herb, Betty, Bob. Again, all conditions are met. Bob is on an aisle, Betty and Herb are sitting together, and James is not sitting next to Jill.
The results of a common standardized test used in psychology research is designed so that the population mean is 135 and the standard deviation is 30. A subject earns a score of 198. What is the z-score for this raw score?
z-score=
Answer:
2.1
Step-by-step explanation:
Mean+z score(Standard deviation)=raw score
Let the z score be z
135+z(30)=198
30z=63
z=2.1
The z-score is a measure of how many standard deviations a score is from the mean. In this case, where the test was designed with a mean of 135 and a standard deviation of 30, a score of 198 results in a z-score of 2.1.
Explanation:The z-score represents how many standard deviations an element is from the population mean. In this particular case, the results of a standardized test designed with a population mean of 135 and a standard deviation of 30 are given. A subject has a test score of 198.
To calculate the z-score, you use the formula: z = (X - μ) / σ. Where X is the score, μ is the mean, and σ is the standard deviation.
Substitute the given values into the formula:
z = (198 - 135) / 30
z = 2.1
So a test score of 198 would yield a z-score of 2.1.
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A square prism has a height of 15 centimeters and a volume of 960 cubic centimeters. What is the measure of the width of the square base
Answer:
8
Step-by-step explanation:
Because if you do 15•8•8 then it equals 960 and the formula for volume is l•w•h
Dev thinks of a whole number. He multiplies it by 4. He rounds his answer to the nearest 10. The result is 50. Write all the possible number that Dev could have started with.
Answer:
{12, 13}
Step-by-step explanation:
Whole numbers that round to 50 will be in the range 45 to 54. Multiples of 4 in that range are 48 and 52.
48 = 4·12
52 = 4·13
Dev's number could be either 12 or 13.
Malcolm is trying a very low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:
50 < 2x + 10 and 2x + 10 < 110
Solve for x in this inequality, and explain what the answer represents.
1. x < 20 and x > 50; Malcolm needs to consume less than 20 grams of carbohydrates or more than 50 grams of carbohydrates.
2. x > 20 and x < 50; Malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.
3. x > 30 and x < 60; Malcolm needs to consume more than 30 grams of carbohydrates, but less than 60 grams of carbohydrates.
3. x < 30 and x > 60; Malcolm needs to consume less than 30 grams of carbohydrates or more than 60 grams of carbohydrates.
Answer:
The correct option is 2.
Step-by-step explanation:
The given inequalities are
[tex]50<2x+10[/tex] .... (1)
[tex]2x+10<110[/tex] .... (2)
Solve each inequality.
Subtract 10 from each side of inequality (1).
[tex]50-10<2x+10-10[/tex]
[tex]40<2x[/tex]
Divide both the sides by 2.
[tex]20<x[/tex]
The value of x is more than 20.
Subtract 10 from each side of inequality (2).
[tex]2x+10-10<110-10[/tex]
[tex]2x<100[/tex]
Divide both the sides by 2.
[tex]x<50[/tex]
The value of x is less than 50.
Since x > 20 and x < 50, therefore Malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.
Hence the correct option is 2.
Answer:
its number 2
Step-by-step explanation:
A musician begins performing concerts. His first concert had 500 people attending. The musician says that if attendance grows by 5% every concert, there will be 650 people at his third concert. Explain why the musician's prediction is incorrect.
Answer:551.25
Step-by-step explanation:
500 x .05 =25+500= 525 which is the second concert. Multiply that by .05 which is 26.25, add that to 525 to get 551.25 which is not 650.
Abby took out a car loan for $10,090 that has a 0% APR for the first 22 months and will be paid off with monthly payments over 5 years. For how many months will Abby be charged interest?
A. 82 months
B. 60 months
C. 22 months
D. 38 months
Answer:
d 38 months
Step-by-step explanation:
Answer:
The correct answer is D. 38 months
Step-by-step explanation:
Abby took out a car loan with monthly payments over 5 years. Each year has 12 months. So the total number of payments will be 5 (years) multiplied by 12 (months).
x=5*12=60 months
The first 22 months are without interest, so the months that have interest are the rest of then.
x'= 60-22= 38 months
How many kilograms are equal to 5000 grams
Answer:
for every 1000 there is 1 kilogram so therefore there are 5 kilograms to equal 5000 grams
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Rewrite the radical expression as an expression with rational exponents.
fifth root of x to the power of 7
Answer:
x^(7/5)
Step-by-step explanation:
Root goes on bottom of fraction
Power goes on top
x^(7/5)
Answer:
[tex]x^{\frac{7}{5}}[/tex]
Step-by-step explanation:
Rewrite the radical expression as an expression with rational exponents.
fifth root of x to the power of 7
[tex]\sqrt[5]{x^7}[/tex]
To write the given expression with radical exponent we use the rule
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
Move the index n to the denominator of exponent
[tex]\sqrt[5]{x^7}=x^{\frac{7}{5}}[/tex]
Expression with rational exponent is [tex]x^{\frac{7}{5}}[/tex]
How to find the legs of a right triangle with only the hypotenuse?
Let x = legs of right triangle.
The set up would be:
x^2 + x^2 = (hypotenuse)^2
Understand?
To find the legs of a right triangle with only the hypotenuse known, the Pythagorean theorem is used. Without extra information like an angle or one leg length, it's impossible to find the specific leg lengths due to the infinite possibilities of right triangle configurations with the same hypotenuse length.
The question involves finding the lengths of the legs of a right triangle when only the length of the hypotenuse is known. Utilizing the Pythagorean theorem, which states that in a right triangle the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), expressed as a² + b² = c². To find the lengths of the legs (a and b) given the hypotenuse (c), one needs additional information such as the angle of the triangle or the length of one of the legs.
Without such information, it is not possible to determine the specific lengths of the legs because there are infinitely many right triangles with different sets of leg lengths that could have the same hypotenuse length. Therefore, to address this problem, one might use trigonometry if any angle is known, or apply other relevant context or given data.
Jace has consumed 1,500 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 1,900 calories per day. How many calories does he have left to consume for the day? Is 1,100 a viable solution to this problem?
===================================
Yes; 1,100 is less than 1,500.
No; 1,100 is more than the 400 he burned off at the gym.
No; 1,100 will cause him to exceed 1,900.
Yes; 1,100 is less than 1,900
Answer:
No, it will cause him to exceed 1900.
Step-by-step explanation:
1,500 - 400 = 1,100 (his total after the gym)
1,100 + 1,100 exceeds 1,900. He wants to keep his total below 1,900, so this is not a viable solution.
Answer:
No; 1,100 will cause him to exceed 1,900.
Step-by-step explanation:
The rationale for this problem is basic.
Jace established a diet restricted to 1900kcal.
If he started 1500kcal and burned 400kcal in the gym, Jane's partial jump is 1100 calories.
Thus, it can still eat the total of 1900-100 = 800kcal.
Any value over 800kcal will exceed the tax threshold and will disrupt Jane's results.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. A survey with a two-point scale was conducted in an organization. It concluded that 85% of the respondents were unsatisfied with the career guidance they were provided. If 2,000 people participated in the survey, people were satisfied with the career guidance. Reset Next
Answer:
300 people were satisfied
Step-by-step explanation:
If 85% were unsatisfied, we assume the remaining 15% were satisfied. That percentage of 2000 is ...
0.15×2000 = 300
Answer:
300
Step-by-step explanation:
PLATO
In the triangles, and .
Which statement correctly compares and ?
and are the same length.
is longer than .
is shorter than .
is shorter than or the same length as .
Answer:
answer is B just got 100%
Step-by-step explanation:
Since BC is parallel to DE, triangles ABC and ADE are similar. What are the lengths of the unknown sides?
A. AC = 14 cm; CE = 8 cm
B. AC = 12 cm; CE = 7 cm
C. AC = 10 cm; CE = 5 cm
D. AC = 5 cm; CE = 10 cm
Answer:
C
Step-by-step explanation:
Step 1: find BC
Given Triangles ABC and ADE are similar,
[tex]\frac{AB}{AD}[/tex] = [tex]\frac{BC}{DE}[/tex]
BC = [tex]\frac{AB}{AD}[/tex] x DE
= [tex]\frac{8}{8 + 4}[/tex] x 9
= 6 cm
Step 2: use Pythagorean theorem to find AC and / or AE
Consider triangle ABC,
by Pythagorean theorem,
AB² + BC² = AC²
AC² = 6² + 8² = 100
AC = √100 = 10 (answer... we can see that C is the only one with AC=10.
Step 3: Verify.. even though we know that it is C because AC = 10, you can verify that the ansewer is correct by finding CE and confirming that CE=5
By using similar triangles ABC and ADE,
AC/AE = AB / AD
AE = AD/AB x AC = 12/8 x 10 = 15
CE = AE - AC = 15 - 10 = 5 (answer confirmed)
What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?
Answer:
14.18 units & 4.88 units
Step-by-step explanation:
The right triangle in this problem is shown in the attached image.
Using trigonometry, the adjacent leg would be 15 Cos 19°
and the opposite leg would be 15 Sin 19°
Thus,
one leg is 15 Cos 19 = 14.18 units, and
another leg is 15 Sin 19 = 4.88 units
Answer:
For plato users the correct option is D.
Step-by-step explanation:
D. 4.9 units, 14.2 units
Problem: an old book listed that 72 turkeys were bought for $\$\square.\square\square$ each, at a total cost of $\$\square 67.9\square.$ what was the cost of each turkey, if each $\square$ stands for a digit that was unreadable in the old book
Answer:
72 turkeys were bought at $5.11 each for a total cost of $367.92.
Step-by-step explanation:
Trial and error isn't so difficult for this problem. The final price will be an even number of cents. Without those pennies added, the price per turkey must be below an integer number of cents, but within 1/8 cent of that integer number.
167.90/72 = 2.3319... (too high)267.90/72 = 3.7208... (too high)367.90/72 = 5.1097... good candidate467.90/72 = 6.4986... (too low)567.90/72 = 7.8875 (too low)667.90/72 = 9.2763... (too low)For higher first digits of the total cost, the per-turkey cost is more than 3 digits.
For our "good candidate", the per-turkey cost will be $5.11, so the total bill will be $5.11×72 = $367.92 . . . . matches the required digits.
Need help with a math question
Answer:
0.000032,0.00000.64
Step-by-step explanation:
For this case, it can be observed that the sequence is performed by multiplying each term by 0.2:
We have to:
[tex]0.1 * 0.2 = 0.02\\0.02 * 0.2 = 0.004\\0.004 * 0.2 = 0.0008\\0.0008 * 0.2 = 0.00016\\0.00016 * 0.2 = 0.000032\\0.000032 * 0.2 = 0.0000064[/tex]
Answer:
The next terms are:
[tex]0.000032\\0.0000064[/tex]
What is the surface area of the regular pyramid below
Answer:
C. 864 units²Step-by-step explanation:
We have the square in the base and four triangles on the lateral surface.
The formula of an area of a square:
[tex]A_{\square}=a^2[/tex]
a - side lenght
We have a = 16. Substitute:
[tex]A_{\square}=16^2=256[/tex]
The formula of an area of a triangle:
[tex]A_{\triangle}=\dfrac{bh}{2}[/tex]
b - base
h - height
We have b = 16 and h = 19. Substitute:
[tex]A_{\triangle}=\dfrac{(16)(19)}{2}=152[/tex]
The Surface Area:
[tex]S.A.=A_{\square}+4_{\triangle}[/tex]
Substitute:
[tex]S.A.=256+4(152)=256+608=864[/tex]
Answer: it C. 864 units²
Step-by-step explanation: I just did it
A cricketer has a mean 58 runs in nine innings.Find out how many runs are to be scoredin the 10th inningd to raise the mean scroce to 61.
Answer:
88
Step-by-step explanation:
Nine innings have a mean of 58 runs, and the tenth inning will have x runs. So the overall mean is:
μ = (9×58 + x) / 10
We want the mean to be 61, so:
61 = (9×58 + x) / 10
610 = 522 + x
x = 88
The cricketer must score 88 runs to raise the mean to 61.
An interval estimate is used to estimate _____.
a. the shape of the population's distribution
b. a sample statistic
c. a population parameter
d. the sampling distribution
Answer:
An estimate of a population parameter that provides an interval of values
believed to contain the value of the parameter is known as the inveral estimate.
Step-by-step explanation:
Therefore, the correct answer C.
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Find an nth degree polynomial function calculator n=4 -1,3,2+4i are zeros
Step-by-step explanation:
By the fundamental theorem of algebra, the degree of the polynomial equals the number of roots (including complex and multiplicities, i.e. multiple roots).
Since n=4, we expect to find 4 roots, although we are only given three, namely -1,3,2+4i.
Fortunately, if the polynomial has real coefficients (which we will ASSUME), for any complex root to exist, its conjugate is also a root to the equation.
Since the conjugate of 2+4i is 2-4i, we now have all four roots, -1, 3, 2+4i, 2-4i.
An n-degree polynomial may be construct by the product of (x-ri) where ri are the roots. This means
P(x) = (x-(-1))(x-3)(x-2-4i)(x-2+4i), which is
P(x) = (x+1)(x-3)(x-2-4i)(x-2+4i)
When expanded, P(x) = x^4-6x^3+25x^2-28x-60
Check:
sum of roots = (-1+3+2+4i+2-4i) = 6 (same as negative of coefficient of term x^3) ok
product of roots = (-1)(3)(2+4i)(2-4i)=-3*20 = -60 = constant term, ok.
Note: kP(x) is also a polynomial with the same four roots, where k=any real number. P(x) is a particular case where k=1.
The 4th degree polynomial with given zeros -1, 3, and 2+4i, can be derived from these roots and is of the form f(x) = a(x+1)(x-3)(x-2-4i)(x-2+4i). Complex roots always appear in conjugate pairs if the coefficients of the polynomial are real numbers.
Explanation:The subject of the question is related to the Mathematics of polynomials. Specifically, the question requests the equation of an nth degree polynomial function with n=4 where the zeros include -1, 3, and 2+4i. Given that we have a 4th degree polynomial and we already have 3 roots, we are missing one more. In mathematics, complex roots always come in pairs, so if 2+4i is one of the roots, then its conjugate 2-4i must also be a root.
So, the four roots are: -1, 3, and 2±4i. The polynomial can then be constructed by setting these roots as factors of the polynomial which would then be of the form:
f(x) = a(x+1)(x-3)(x-2-4i)(x-2+4i)
Where 'a' is a constant that will be 1 if the leading coefficient is not specified in the problem.
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Situation:
Find the age of the skull to the nearest year,
Enter the correct answer.
A hiker in Africa discovers a skull that
contains 32% of its original amount of C-
14.
DONE
N = Noekt
00000
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
K = 0.0001
t = time, in years
Answer:
11,394 years old
Step-by-step explanation:
The equation looks like this:
[tex]N=N_{0}e^{kt}[/tex]
The only thing left up to us is to decide what value should go in for N. Since we are told that 32% of the original amount is what the hiker finds, we are operating in percentages. Before any decomposition took place, the amount of skull was 100%. Filling in now we have:
[tex]100=32e^{.0001t}[/tex]
Divide both sides by 32 to get
[tex]3.125=e^{.0001t}[/tex]
In order to get that t out of the exponential position that it is currently in, we will take the natural log of both sides, since a natural log "undoes" an e (that is because the base of a natural log is e). Taking the ln of both sides and utilizing that rule for natural logs and e's gives us:
ln(3.125) = .0001t
Divide both sides by .0001 to get that
t = 11,394 years
I DONT WANT TO FAIL!!!! PLEASE HELP ME WITH THE CORRECT ANSWER, WILL MARK AS BRAINLIEST!!!
What is the solution to the system of linear equations? {4x+3y=543x+9y=108 Enter your answer in the boxes.
Answer:
x = -24
y = 66
Step-by-step explanation:
12x+9y = 102
12x+16y = 432
---------------------
y = 66
4x + (66*3) = 102
198-102 = -96
-96 / 4 = -24
Answer:
solution is [tex](6,10)[/tex]
Step-by-step explanation:
[tex]4x+3y=54[/tex]
[tex]3x+9y=108[/tex]
WE use elimination method to solve for x and y
Multiply the first equation by [tex]-3[/tex]
[tex]-12x-9y=-162[/tex]
[tex]3x+9y=108[/tex]
Now add both the equations, we will get
[tex]-9x=-54[/tex]
Divide by [tex]-9[/tex] on both sides
[tex]x=6[/tex]
Now we plug in the x value in first equaiton and find out y
[tex]4x+3y=54[/tex]
[tex]4(6)+3y=54[/tex]
[tex]24+3y=54[/tex], subtract 24 on both sides
[tex]3y=30[/tex]
Divide both sides by 3
[tex]y=10[/tex]
So solution is [tex](6,10)[/tex]
Find the measure of angle ABC.
A. 124
B. 97
C. 56
D. 51
Answer D. 51
Step-by-step explanation:
Sum of the interior angles of a triangle is up to 180
.: 32+(2x-15) + (x-5) = 180
Group like terms
2x+x =180 - 32 + 15 + 5
When - and + sign cross equal sign it turns to the opposite
3x = 168
x= 168/3
.: X =56
Now put x = 56 in (x - 5)
Angle ABC = 51
Based on the model N(1154,81) describing steer weights, what are the cutoff values for
a) the highest 10% of the weights?
b) the lowest 20% of the weights?
c) the middle 40% of the weights?
what is the measure of at in oo below
Answer:
Step-by-step explanation: