Answer:
X = -8 X= -4
Step-by-step explanation:
x² + 12x = -32
(x + 12/2)² = -32 + (12/2)²
(x + 6)²= 4
square root both sides
x + 6 = 2
x + 6 = -2
x=-8 x=-4
For the function f shown in the graph below, what is the local minimum? Question
Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function?
Select all correct answers.
Select all that apply:
{(4,9),(0,−2),(0,2),(5,4)}
{(5,−5),(5,−4),(7,−2),(3,8)}
{(4,3),(8,0),(5,2),(−5,0)}
{(6,9),(9,−4),(6,1),(−5,11)}
{(4,12),(2,6),(−5,6),(3,−2)}
18 students each collected the same number of Cans for a project. If the students collected a total of 306 cans, how many cans did each student Collect?
Using division operation, the number of cans collected by each of the 18 students is 17.
What is division operation?Division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
Division operation involves the dividend (the number being divided), the divisor (the number dividing the dividend), and the product called the quotient.
The total number of students engaged in the can collection project = 18
The total number of cans collected = 306
The number of cans collected by each, if each collected the same quantity = 17 (306 ÷ 18)
Thus, based on a division operation, the number of cans each student collected is 17.
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Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 193 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.90 cm, y=81.47 kg, r=0.303, P-value=0.002, and y=−107+1.13x. Find the best predicted value of y (weight) given an adult male who is 153 cm tall. Use a 0.01 significance level.
Answer:
At a 0.01 significance level, we reject the null hypothesis and conclude that the predicted weight of 65.89 kg is significantly different from the actual weight, which could be anywhere between 53.45 kg and 78.32 kg.
Step-by-step explanation:
Given the linear regression equation:
y = -107 + 1.13x
where x is the height in cm and y is the weight in kg.
To find the predicted value of y for a person with a height of 153 cm, we substitute x = 153 into the regression equation:
y = -107 + 1.13(153)
y = -107 + 172.89
y = 65.89
Therefore, the best predicted weight for an adult male who is 153 cm tall is 65.89 kg.
To check if this predicted value is statistically significant at a 0.01 significance level, we can perform a hypothesis test.
Null Hypothesis: The predicted weight for a person with a height of 153 cm is not significantly different from the actual weight.
Alternative Hypothesis: The predicted weight for a person with a height of 153 cm is significantly different from the actual weight.
We can use a t-test to test this hypothesis, with the test statistic:
t = (y_predicted - y_actual) / (s / sqrt(n))
where y_predicted is the predicted weight, y_actual is the actual weight, s is the standard error of the estimate, and n is the sample size.
The standard error of the estimate can be calculated using:
s = sqrt((1 - r^2) * Sy^2)
where Sy is the sample standard deviation of the y variable.
From the given information, we have:
Sy = 22.77 kg
r = 0.303
Therefore,
s = sqrt((1 - 0.303^2) * 22.77^2) = 20.19 kg
The sample size is n = 100.
Substituting these values into the t-test formula, we get:
t = (65.89 - y_actual) / (20.19 / sqrt(100))
t = (65.89 - y_actual) / 2.019
We want to test at a 0.01 significance level, which corresponds to a two-tailed test with a critical value of t = ±2.576 (from a t-distribution with 98 degrees of freedom, since n-2=98).
If the absolute value of t is greater than 2.576, we reject the null hypothesis and conclude that the predicted weight is significantly different from the actual weight.
Substituting t = 2.576 and t = -2.576 into the t-test formula, we get:
2.576 = (65.89 - y_actual) / 2.019
y_actual = 53.45 kg
-2.576 = (65.89 - y_actual) / 2.019
y_actual = 78.32 kg
Therefore, at a 0.01 significance level, we reject the null hypothesis and conclude that the predicted weight of 65.89 kg is significantly different from the actual weight, which could be anywhere between 53.45 kg and 78.32 kg.
The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = Sqrt 2 + t , y = 1 + 1 /2 t, where x and y are measured in centimeters. The temperature function satisfies Tx(2, 9) = 7 and
Ty (2, 9) = 1. How fast is the temperature rising on the bug's path after 2 seconds? (Round your answer to two decimal places.)
The temperature is rising at a rate of 7.5 degrees Celsius per second along the bug's path after 2 seconds.
What is differentiation?A derivative of a function with regard to an independent variable is defined as differentiation. In calculus, differentiation can be used to calculate the function per unit change in the independent variable.
We can use the chain rule of differentiation to find how fast the temperature is changing on the bug's path. Let T denote the temperature function, and let x and y be functions of time t given by x = sqrt(2) + t and y = 1 + t/2. Then the temperature function on the bug's path is given by T(x(t), y(t)), and we want to find dT/dt at t = 2.
Using the chain rule, we have:
dT/dt = dT/dx * dx/dt + dT/dy * dy/dt
We are given Tx(2, 9) = 7 and Ty(2, 9) = 1, so we can evaluate the partial derivatives at (x, y) = (2, 9):
dT/dx(2, 9) = 7
dT/dy(2, 9) = 1
To find dx/dt and dy/dt, we can take the derivatives of x and y with respect to t:
dx/dt = 1
dy/dt = 1/2
Now we can plug in the values:
dT/dt = 7 * 1 + 1 * 1/2
dT/dt = 7.5
Therefore, the temperature is rising at a rate of 7.5 degrees Celsius per second along the bug's path after 2 seconds.
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Some states now allow online gambling. As a marketing manager for a casino, you need to determine the percentage of adults in those states who gamble online. How many adults must you survey in order to be 99% confident that your estimate is in error by no more than three percentage points? Complete parts (a) and (b) below. a. Assume that nothing is known about the percentage of adults who gamble online. n= (Round up to the nearest integer.)
The sample size for part (a) is 2401, and the sample size for part (b) is 1417 if the margin of error is no more than two percentage points and use a confidence level of 95%
We have,
It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.
The formula for finding the MOE:
MOE =Z_{score} * s/√n
Where Z_{score} is the z score at the confidence interval
s is the standard deviation
n is the number of samples.
We have:
MOE = 2% = 0.02 and
α = 1-0.95 = 0.05
Let's assume the value of p = 0.5, and q = 0.5
From the table:
Z_(0.05/2)
= Z_(0.025)
= 1.96
n = 2401
For part (b):
p = 18% = 0.18, and q = 0.82
so, we get,
n = 1417.5 = 1417
Thus, the sample size for part (a) is 2401, and the sample size for part (b) is 1417 if the margin of error is no more than two percentage points and use a confidence level of 95%
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CAN SOMEONE HELP WITH THIS QUESTION?
Answer:
X2 = 1.697916 X3 = 1.431
Step-by-step explanation:
use Newton's formula of the method of approximating of zeros of a function : x_n+1. = x_n - f(x_n)/f'(x_n)
A fair die with sides labeled 1 through 6 is rolled two times. The values of the two
rolls are added together. The sum is recorded as the outcome of a single trial of a
random experiment. Compute the probability that the sum is greater than 10.
A fair die is rolled twice, then the probability that the sum is greater than 10 is 1/12.
Finding the total number of possible outcomes when the dice is rolled twice:
A total of 6*6 = 36 outcomes are possible as there are 6 outcomes for the first roll and 6 outcomes for the second.
Making a list of all results that add up to greater than 10:
5 + 6 = 11
6 + 5 = 11
6 + 6 = 12
There are only three favorable outcomes.
So, the probability of getting a number greater than 10 =
[tex]\frac{no\ of\ favorable\ outcomes}{total\ number\ of\ possible\ outcomes}[/tex]
P(sum > 10) = 3/36 = 1/12
Therefore, there is a 1/12 probability that the sum of the two dice is greater than 10.
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AM
XYZ Homework
Use the fundamental identities to match equivalent expressions.
a
d
с
b
1
sec (0) + 1
1
1
+
1 - cos(0) 1 + cos(0)
+
G VIDEO
1
csc (0) - cot (0)
1
csc (0) + 1
1
sec(0) - 1
+
1
csc (0) + cot(0)
1
csc (0) - 1
O Port to forum
a. 2 csc (0)cot (0)
b. 2 sec (0)tan (0)
c. 2 cot (0)
d. 2 csc² (0)
Using the fundamental identities, the equivalent expressions are hereby matched as follows:
a. 2 csc (θ) cot (θ) = 2 sin²(θ) / (sin(θ) + cos(θ))
b. 2 sec (θ) tan (θ) = (2 sec²(θ)) - 2 sec(θ)
c. 2 cot (θ) = 2 / sin(θ) - csc(θ)
d. 2 csc² (θ) = 2 / (csc(θ) - 1)(csc(θ) + 1)
How did we arrive at these expressions?Using the fundamental identities, rewrite each expression as follows:
a. 2 csc (θ) cot (θ) = 2 / sin(θ) * cos(θ) = 2 cos(θ) / sin(θ) = 2 / sin(θ) - 2 / sin(θ) + 2 cos(θ) / sin(θ) = 2 / sin(θ) - 2 / (1 + cot(θ)) = (2 - 2 sin(θ)) / (sin(θ) + cos(θ)) = (2 sin²(θ)) / (sin(θ) + cos(θ))
b. 2 sec (θ) tan (θ) = 2 / cos(θ) * sin(θ) / cos(θ) = 2 sin(θ) / cos²(θ) = 2 / cos²(θ) - 2 / cos(θ) = (2 sec²(θ)) - 2 sec(θ)
c. 2 cot (θ) = 2 cos(θ) / sin(θ) = 2 / sin(θ) - 2 / sin²(θ) = 2 / sin(θ) - csc(θ)
d. 2 csc² (θ) = 2 / sin²(θ) = 2 / (1 - cos²(θ)) = 2 / (1 - cos(θ))(1 + cos(θ)) = 2 / (csc(θ) - cot(θ))(csc(θ) + cot(θ)) = 2 / (csc(θ) - 1)(csc(θ) + 1)
Therefore, the matches are:
a. 2 csc (θ) cot (θ) = 2 sin²(θ) / (sin(θ) + cos(θ))
b. 2 sec (θ) tan (θ) = (2 sec²(θ)) - 2 sec(θ)
c. 2 cot (θ) = 2 / sin(θ) - csc(θ)
d. 2 csc² (θ) = 2 / (csc(θ) - 1)(csc(θ) + 1)
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1.2 A Telkom account holder notices that her phone bills for three consecutive months were
significantly different. In May, her account was one and a half times more than her account in June.
Her account in July was R 50 more than her account in June. In total, she spent R 575 in cellular-
phone accounts in the three months. What was her account for each month?
The balance on the account of the Telkom account holder, every month was :
May - R 225June - R 150July R 200How to find the account balance ?We know that May was one and half times June :
M = 1. 5 x J
July was R 50 more than June :
L = J + 50
Total spent was R 575 :
M + J + L = R 575
Then we can solve by substitution:
( 1. 5 J ) + J + ( J + 50 ) = 575
3. 5 J + 50 = 575
3. 5 J = 525
J = 525 / 3. 5 = R 150
L would be:
= 150 + 50
= R 200
M would be:
= 1. 5 x 150
= R 225
The balances for the Telkom account holder is therefore May - R 225, June - R 150, and July R 200.
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A particular sound wave can be graphed using the function y=-1 sin 5x. Find the period of the function.
We refer to a function as periodic if it repeats across time with a fixed interval.
It is written as f(x) = f(x + p), where p denotes the function's period and is a real number.
Period is defined as the elapsed time between the two instances of the wave.
Here, we have,
A function's period is the amount of time between repetitions of the function. A trigonometric function's period is defined as the length of one complete cycle.
A periodic function is one whose values repeat at regular intervals. For instance, periodic functions include the trigonometric functions, which repeat every 2 pi radians.
Waves, oscillations, and other periodic events are all described by periodic functions in science. A period is the amount of time that separates two waves, whereas a periodic function is a function that repeats its values at regular intervals.
Each set of numbers that are separated by a comma in a number when expressed in standard form is known as a period. It has four periods, making it 5,913,603,800. The place value chart displays each period using a distinct color.
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URGENT!! I WILL GIVE
BRAINLIEST!!!!! AND ALSO 100 POINTS!!!!!
Answer: All of the slopes are the same.
Which function includes the minimum or maximum value of f as a number that appears as it is shown?
a) f(x)=(x+2)^{2}−16
b) f(x)=(x−2)(x+6)
c) f(x)=x^{2}+4x−12
d) f(x)=x^{2}+6x−2x−12
NEED HELP PLEASE NOW
Answer:
im pretty sure its the first one that you chose :)
Step-by-step explanation:
Find the size of the following angles
Step-by-step explanation:
Q1. By linear pair, I know that 72* + unknown angle = 180*
therefore unknown angle = 180-72 = 108*
Now because this is a pentagon, the total of all interior angles of a polygon equals 540*
so 108* + 100* + 110* + 45* (Half of 90 , written as a semi-square) + Y* = 540
Y* = 540 - 363 = 177*
Q2. 360 - (80+70+110) = q
q = 360 - 220 = 140*
Q3. 160+160+ S* = 360*
360* - 320* = S*
S* = 40*
Hope it helps
What integer is the square root of 115 closest to?
Answer:
10
Step-by-step explanation:
draw a net for making a rectangular prism 5cm by 3cm by 1cm
Here is a net for making a rectangular prism with dimensions of 5 cm by 3 cm by 1 cm:
________
/ / |
/ / |
/_______ / |
| | |
| | |
| | |
| | /
| | /
|________|
The above net consists of six rectangles, where the first rectangle represents the base of the prism with dimensions of 5 cm by 3 cm, and the remaining five rectangles represent the sides of the prism.
What is a rectangular prism?A rectangular prism, also known as a rectangular cuboid, is a three-dimensional geometric shape that has six rectangular faces, where each face meets at right angles with its adjacent faces.
It is common in everyday objects such as boxes, books, and bricks, and they are used in various applications in mathematics, physics, engineering, etc.
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Hudson measure the volume of a sink basin by modeling it as a hemisphere. Hudson measures its circumference to be 91 3/4 inches. Find the sink's volume in cubic inches.
Round your answer to the nearest tenth if necessary.
Rounding to the nearest tenth, the sink's volume is approximately [tex]6328.2[/tex] cubic inches.
What is the Hudson measures?The circumference of a hemisphere is represented by the formula:
[tex]C = 2 \pi r[/tex]
here C is the circumference and r is the radius of the hemisphere.
it is given that the circumference C as [tex]91 3/4[/tex] inches. now convert into a decimal
[tex]91 3/4 inches = 91.75 inches[/tex]
we are having
[tex]91.75[/tex] inches [tex]= 2πr[/tex]
Solving for r, we get:
[tex]r = 91.75 / (2\pi) \approx 14.599[/tex] inches (rounded to three decimal places)
The volume of a hemisphere is represented by formula
[tex]V = (2/3)\pir^3[/tex]
Substituting our value of r, we get:
[tex]V = (2/3)\pi(14.599)^3 \approx 6328.2[/tex] cubic inches
Therefore, rounding to the nearest tenth, the sink's volume is approximately [tex]6328.2[/tex] cubic inches.
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How many solutions can be found for the equation 3y + 5 − 2y = 1
We can solve the equation to find it's number of solutions, but we already know it only has 1 solution because it is a linear equation (y is raised to the first power).
[tex]3y + 5 - 2y = 11[/tex]
[tex]y + 5 = 11[/tex]
[tex]y = 6[/tex]
This confirms that there is only 1 solution.
Teresa bought 6 CDs that were each the same price. Including sales tax, she paid a total of 84.60 . Each CD had a tax of 0.80 . What was the price of each CD before tax?
Answer:0.70
Step-by-step explanation:
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #3
Answer:
The graph will be translated down 2 units.
The new horizontal asymptote is y=2 because the graph now crosses over the y axis at 2. This is at the point (0,2).
ng
he
34. The dimensions of Dawn's porch are shown.
Dawn's Porch
6 feet
A
B
6 feet
A. 32
2 feet
11 feet
What is the area, in square feet, of Dawn's porch?
B. 42
2 feet
C. 46
D. 50
Answer:
[tex]the \: answer \: for \: the \: question \: is \: 50[/tex]
QUICKLY HELP PLEASE ITS VERRY MUCH SO APPREICATED
The mean absolute deviation (MAD) of the data set include the following: A. 11.
How to calculate the mean absolute deviation?In Mathematics, MAD is an abbreviation for mean absolute deviation and the mean absolute deviation (MAD) of a data set can be calculated by using this formula;
MAD = 1/n ∑|x - μ|
Where:
n represents the number of data (observed values)μ represents the mean of the data set.x represents the individual data (values).By substituting the given parameters into the MAD formula, we have the following;
MAD = 1/10 [(325 - 290) + (310 -290) +(289-290)+(288-290)+(285-290)+(285-290)+(285-290) + (280-290) + (280-290) + (273-290)]
MAD = 1/10(35 + 20+1+2+5+5 +5 + 10 + 10 + 17).
MAD = 1/10(110)
MAD = 11
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The cost in dollars to produce x shovels in a factory is given by the function C(x)=33x+430. The number of shovels that can be produced in h hours is given by the function N(h)=30h
7. Find the rule for C(N(h)).
8. Find the cost when h=12 hours
Okay, to find the maximum number of shovels that can be produced with $10,000, we need to do the following:
1) Set the cost function C(N(h)) = 10,000. So: 990h + 430 = 10,000
2) Subtract 430 from both sides: 990h = 9,570
3) Divide both sides by 990: h = 9.75 (round to 10 hours)
4) Substitute 10 hours into the function for number of shovels:
N(10) = 30(10) = 300 shovels
Therefore, the maximum number of shovels that can be produced with $10,000 is 300 shovels.
Let me know if you have any other questions!
Evaluate pqr - s2t, if p = -2, q = 5, r = -7, s = 0, and t = 4.
I need help fast!!
The answer of the given expression is 70.
What is the meaning of Evaluation?Evaluation refers to the process of assessing, examining, or appraising something to determine its worth, effectiveness, or quality. It involves the systematic and objective assessment of various aspects or criteria to form an informed judgment or opinion.
What is known by expression?An expression refers to a combination of numbers, symbols, and mathematical operations that represents a mathematical computation or relationship. It can be as simple as a single number or variable, or it can be more complex involving multiple terms, operations, and functions.
we have to find pqr-s2t:
if p=-2, q=5, r=-7, s=0, t=4
putting values in the expression we get
-2×5×(-7)-0×2×4= 70
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The probability of winning a profit of twice your wager is 1/6, the probability of winning a profit equal to your wager is 1/3, and all other probabilities of winning are zero. What is your expected value for this game? Assume the wager is $1.
The expected value for the game is 2/3.
What is expected value?The average value we would anticipate to find if we repeated an experiment several times is the anticipated value of a random variable. It is calculated by averaging the outcomes of multiplying each potential result of the random variable by the associated probability. In other words, it's the weighted average of all potential possibilities, with the weights being the likelihoods that each outcome would actually happen. In several disciplines, including finance, economics, and engineering, predictions and judgements are made using the expected value, a fundamental idea in probability theory.
Let us suppose the profit = X.
Thus,
Probability of winning twice our wager = 1/6 thus, the expected value is:
(2)(1/6) = 1/3
No, for profit equal to wager we have:
(1)(1/3) = 1/3
The total expected value is:
E(X) = (1/3) + (1/3) + 0 = 2/3
Hence, the expected value for the game is 2/3.
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The distance between Eilat and Jerusalem is 292 kilometers. Give this distance in miles. Round the answer to the nearest tenth.
This distance in miles is 181.3 miles.
It's worth noting that the conversion factor of 1 kilometer equals 0.621371 miles is an exact value defined by international agreement, so there is no rounding involved in the conversion itself. The rounding occurs only when expressing the result in a specific number of decimal places. It's also worth noting that conversions between units of measurement are important in many fields, including science, engineering, and international trade.
To convert kilometers to miles, we can use the conversion factor of 1 kilometer equals 0.621371 miles. Therefore, to find the distance between Eilat and Jerusalem in miles, we can multiply the given distance of 292 kilometers by 0.621371:
292 km × 0.621371 = 181.344052 miles
Rounding this result to the nearest tenth gives:
181.3 miles
Therefore, the distance between Eilat and Jerusalem is approximately 181.3 miles.
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10. A flagpole is supported by two identical wires. What is the distance (X) between the two wires?
Using the Pythagoras theorem, we can find the value of x to be = 10ft.
Option B is correct.
Define Pythagoras theorem?The right-angled triangle's three sides are related in line with the Pythagoras theorem, also referred to as the Pythagorean theorem. The hypotenuse of a triangle's other two sides add up to a square, according to the Pythagorean theorem, which states that.
Here in the question,
We have 2 right-angled triangles.
So, base of the large triangle, x
= √ (13² - 12²) + √ (13² - 12²)
= √ 5² + √ 5²
= 5 + 5
= 10ft.
Therefore, the length of the side, x = 10ft.
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4. You have been offered $3,000 in 4 years for providing $2,000 today into a business venture with a friend. If interest rates are 10%, is this a good investment for you?
Step-by-step explanation:
To determine if this is a good investment, we can use present value calculations to see what the $3,000 payment in 4 years is worth today:
Present value of $3,000 in 4 years at 10% interest rate = $3,000 / (1 + 0.10)^4 = $2,102.50.
If we invest $2,000 today and get a payment of $2,102.50 in 4 years, our net gain would be:
Net gain = $2,102.50 - $2,000 = $102.50
Therefore, investing $2,000 today with an interest rate of 10% and receiving $3,000 in 4 years would yield a net gain of $102.50.
While any gain is better than no gain, a return of $102.50 on an investment of $2,000 over a period of 4 years may not be considered a great investment. It's up to the individual to decide whether they feel that the potential gain is worth the initial investment and risk involved.
Solve the percent word problem below:
John invested in a savings bond for 4 years and was paid simple interest at an annual rate of 4%. The total interest that he earned was $48. How much did he invest?
the principal or invested amount is $41.38
The computation of the invest amount is given below:
As we know that
Principal = Amount ÷ (1 + rate × time)
= $48 ÷ (1 + 0.04 × 4)
= $48 ÷ 1.16
= $41.38
Hence, the principal or invested amount is $41.38
Basically we have applied the above formula so that the same would be calculated