Answer:
A
Step-by-step explanation:
X is less than -7 because the open circle indicates that x is not -7
f(x) = x² + 6x-4
g(x) = 2x - 8
Find: (fog)(x)
fog(x) =4x²+44x+12,
f(x) is quadratic function whose value is x²+6x -4 at x.
so , we have asked the value of f(x) at x=g(x) , which another function whose value is 2x-8 .
so, by the concept of composition of functions we have to put the value 2x-8 in place of x in the f(x) function to get fog(x).
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can someone one help me
Answer: Do letter D
Step-by-step explanation:
6-4n = -4 times (n-1)
6-4n = -4n + 1 (because the negatives in 4 and 1 cancel out and make it positive 4 because 1 times 4 is 4)
6-4n = -4n+4
+4 +4
Which gives you
6=4
Answer: No solution
the mean life of a television set is 121 months with a variance of 256 . if a sample of 95 televisions is randomly selected, what is the probability that the sample mean would be less than 118.8 months? round your answer to four decimal places. answer
The probability that the sample mean of a randomly selected sample of 95 televisions would be less than 118.8 months, given a population mean of 121 months and a variance of 256, can be calculated using the Central Limit Theorem. The calculated probability is 0.1151, rounded to four decimal places.
According to the Central Limit Theorem, the sample mean of a large enough sample size from any population will follow a normal distribution, regardless of the shape of the population distribution. Since the sample size is large (n = 95), we can use the normal distribution to approximate the probability.
The mean of the sample mean is equal to the population mean, which is 121 months. The standard deviation of the sample mean, also known as the standard error, can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population variance is given as 256, so the standard deviation is √256 = 16. Therefore, the standard error is 16 / √95 ≈ 1.645.
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Jude types 840 characters in 5 minutes. What is her typing rate in characters per minute?
If you square my age and subtract 28 times my age, the result is 60. What is my age?
My age is 2 years from the given condition.
Given that, if you square my age and subtract 28 times my age, the result is 60.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let x be my age.
Now, square my age is x²
28 times my age =28x
The square of my age and subtract 28 times my age, the result is 60.
x²-28x=60
⇒ x²-28x-60=0
⇒ x²+30-2x-60=0
⇒ x(x+30)-2(x+30)=0
⇒ (x+30)(x-2)=0
⇒ x=2
Hence, my age is 2 years from the given condition.
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Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean = 246 days and standard deviation 13 days. Complete parts (a) through (1) below
(a) What is the probability that a randomly selected pregnancy lasts less than 242 days?
The probability that a randomly selected pregnancy lasts less than 242 days is approximately (Round to four decimal places as needed)
a
ANSWER
0.3783
EXPLANATION
The lengths of the pregnancies, X, is normally distributed with a mean of 246 days and a standard deviation of 13 days,
\(X=N(246,13)\)We have to find the probability that a randomly selected pregnancy lasts less than 242 days,
\(P(X<242)=?\)For this, we have to standardize the variable X with the formula,
\(Z=\frac{X-\mu}{\sigma}\)So the probability we have to solve is,
\(P(X<242)=P\mleft(\frac{X-\mu}{\sigma}<\frac{242-\mu}{\sigma}\mright)=P\mleft(Z<\frac{242-246}{13}\mright)=P(Z<-0.31)\)This is equivalent to,
\(P(Z<-0.31)=P(Z>0.31)\)Which is also equivalent to,
\(P(Z>0.31)=1-P(Z<0.31)\)We have to find these equivalences because, usually, normal distribution tables show the probabilities for positive z-scores and to the left of those values - i.e. less than those values. Find z = 0.31 in a z-table,
So, the probability is,
\(P(X<242)=1-P(Z<0.31)=1-0.6217=0.3783\)Hence, the probability that a randomly selected pregnancy lasts less than 242 days is 0.3783.
Which of the following best describes the relationship between the number of miles a person runs and the number of calories he/she burns?
A. neither correlation nor causation
B. correlation and causation
C. correlation without causation
D. causation without correlation
2. Un auto viaja a 60 km/h y se detiene a los 2 segundos. qué distancia recorrió en el
frenado? ¿qué aceleración adquirió? ¿Si la aceleración es positiva o negativa, explica
por qué?
Se calcula que la aceleración es - 8,35 m/s.
¿Qué es la aceleración?Ahora sabemos lo siguiente de la pregunta;
Velocidad inicial (u) = 60 km/h o 16,7 m/s
Tiempo empleado (t) = 2 s
Dado que;
v = tu + en
v = 0 m/s porque el carro se detenía
tu = -en
a = -(u/t)
a= -1(6,7 m/s/2 s)
a =- 8,35 m/s
La aceleración es negativa porque la velocidad disminuye con el tiempo.
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A student claimed that reflect a triangle in a line, translating a triangle , rotating a triangle, and reflecting it in a point result in an image that is congruent to the original( pre-image) triangle. explain why they are correct.
If we reflect a triangle in a line, translate a triangle, rotate a triangle, and reflect it in a point result in an image that will be congruent to the original( pre-image) triangle.
This is a problem from triangular geometry. We can solve this problem by following a few steps.
Here a triangle ABC is given and the triangle is at first reflected and then translated, thereafter it rotates and is later reflected.
After all, these processes the value of ∠A, ∠B, and ∠ C remains the same as usual concerning ∠A''', ∠B''', ∠ and C'', as they just changes coordinates not geometric structures.
After all these processes the length of the triangle AB, AC, BD, and A'''B''', B'''C''', C'''A''' remains the same as usual.
∵ We can conclude that ΔABC ≅ ΔA'''B'''C'''
( As AB = A'''B''', BC = B'''C''', ∠ABC = ∠ A'''B'''C''' )
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FILL IN THE BLANK What is the minimum product of two numbers whose difference is 48? What are the numbers?
The minimum product is_____
The two number yield this product?______
Simplify your answer
There are no specific numbers to provide, and the minimum product is undefined in this case.
The minimum product of two numbers whose difference is 48 is obtained when the two numbers are consecutive integers. Let's represent the smaller number as x.
The next consecutive integer would be x + 1. The difference between these two numbers is (x + 1) - x = 1.
According to the given information, the difference between the two numbers is 48. So we have the equation:
x + 1 - x = 48
Simplifying the equation, we find:
1 = 48
This equation is not solvable, as it leads to an inconsistency. It means that there are no two numbers whose difference is exactly 48. Therefore, there are no specific numbers to provide, and the minimum product is undefined in this case.
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Question 3 of 10
What is the quotient of the following division problem?
20652+657 = ?
OA. 31 r286
B. 32 r284
OC. 31 r285
OD. 30 r285
SUBMIT
2. Find the next two numbers in Karina's number pattern. Describe the pattern and explain how you found it.
Answer:
She multiplies each number by three. So 54×3=162
In the diagram, BC = 9. Find AB and AC by dragging the correct distance to its corresponding side?
Answer is: AC= 9\(\sqrt{3}\) Units, AB = 18 units.
What is triangle?Triangles have three interior angles that add up to 180 degrees, and they can be classified based on the lengths of their sides and the measures of their angles.
In ΔABC, angle C is right angle,
so the triangle is right angle triangle;
tan30° = BC/AC
\(\frac{1}{\sqrt{3} }\) = 9/AC
AC= 9\(\sqrt{3}\) Units
and
Sin 30° = BC/AB
1/2 = 9/AB
AB = 18 units
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this problem is difficult and i dont want homework
Answer:
The area is 49/12 or 4 1/12
Step-by-step explanation:
The area of a triangle is:
a = 1/2 × base × height
a = 1/2 × 3 1/2 × 2 1/3 (4 2/3 is not the height!)
a = 1/2 x 7/2 x 7/3 (I converted all the fractions into improper fractions)
a = 49/12 (1 × 7 × 7 = 49, 2 × 2 × 3 = 12)
You can convert it back to a mixed number:
49/12 = 4 1/12
Hope this helps!
Use the number line below to determine which of the following answer choices has statements that are all true
Answer: the last one
Step-by-step explanation: B REPRESENTS
-2 ½ . POINT D REPRESENTS 1 ¾ .
1 ¾ is bigger than -2 ½
The answer choice that has the statement that is true about the number line can be seen in the first option.
What is a number line?A number line is a pictorial representation of lines on a calibrated straight line that serves as a basis for expressing real numbers on a straight line.
We should equally note that:
The left-hand side is the negative x-axis and,The right-hand side is the positive x-axis.From the given figures;
Point A lies to the negative axis direction on point scale 4 i.e -4Point D lies extremely to another point scale so we can say it is \(\mathbf{1 \dfrac{3}{4}}\)Since 3/4 is roughly 0.75 = 1 + 0.75 = 1.75Therefore, we can conclude that Point A represents -4, Point D represents \(\mathbf{1 \dfrac{3}{4}}\) and \(\mathbf{1 \dfrac{3}{4}}\) > -4.
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What are the two solutions of 2x2 = –x2 – 5x – 1?
Answer:
Step-by-step explanation:
quadratic formula
x = -(-5)+
I have a feelings that it’s D but I am not sure. Please be honest and help!
consuela is displaying a cylindrical case on a pedestal. she wants it to be placed so that there is an even amount of space on either side of the case. if the volume of cylinder shown is 1,130.97 cubic inches, how much space will be on either side if its placed on a pedestal that is 18 inches across? round to the nearest inch
The space that will be on either side if its placed on the pedestal of the cylinder that is 18 inches across will be 4.47 inches.
How to compute the dimension?It should be noted that the volume of a cylinder is given as:
= πr²h
We'll then slot the values given into the formula. This will be:
Volume = πr²h
1130.97 = (3.14 × r² × 18)
1130.97 = 56.52r²
r² = 1130.97/56.52
r² = 20
r = ✓20
r = 4.47
In conclusion, the space will be 4.47 inches.
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1. In each of the following cases, which would probably be higher, the mean or the median, or would they be about equal?
a. Salaries in a company employing 100 factory workers and 2 highly paid executives
b. Ages at which residents of a suburban city die, including everything from infant deaths to the most elderly
c. Prices of all new cars sold in 1 month in a large city
d. Heights of all 7-year-old children in a large city
e. Shoe sizes of adult women
Answer:
Check below
Step-by-step explanation:
a. Salaries in a company employing 100 factory workers and 2 highly paid executives: The mean (average) salary would probably be higher than the median salary because the 2 highly paid executives would greatly increase the overall average salary, but would not greatly affect the median salary, which is the middle value when the data is arranged in order.
b. Ages at which residents of a suburban city die, including everything from infant deaths to the most elderly: The median age at death would probably be higher than the mean age at death because the mean age at death would be affected by infant deaths and other early deaths, while the median age at death would be the middle value of the data set when arranged in order.
c. Prices of all new cars sold in 1 month in a large city: The mean and median prices would probably be about equal because the data set is likely to be normally distributed, which means that the mean and median values would be similar.
d. Heights of all 7-year-old children in a large city: The mean and median heights would probably be about equal because the data set is likely to be normally distributed.
e. Shoe sizes of adult women: The mean and median shoe sizes would probably be about equal because the data set is likely to be normally distributed.
The distribution would tend to skew to the left (meaning a lot more people die in the older ages than in the younger ages), hence the median would be higher than the mean.
a. Salaries in a company employing 100 factory workers and 2 highly paid executives: The mean (average) salary would probably be higher than the median salary because the 2 highly paid executives would greatly increase the overall average salary, but would not greatly affect the median salary, which is the middle value when the data is arranged in order.
b. Ages at which residents of a suburban city die, including everything from infant deaths to the most elderly: The median age at death would probably be higher than the mean age at death because the mean age at death would be affected by infant deaths and other early deaths, while the median age at death would be the middle value of the data set when arranged in order.
c. Prices of all new cars sold in 1 month in a large city: The mean and median prices would probably be about equal because the data set is likely to be normally distributed, which means that the mean and median values would be similar.
d. Heights of all 7-year-old children in a large city: The mean and median heights would probably be about equal because the data set is likely to be normally distributed.
e. Shoe sizes of adult women: The mean and median shoe sizes would probably be about equal because the data set is likely to be normally distributed.
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After 4 years, $20,000 deposited in a savings account with simple interest had earned $800 in interest. What was the interest rate?
The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.
We can use the formula for simple interest to solve the problem:
Simple interest = (Principal * Rate * Time) / 100
where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.
We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:
$800 = (20,000 * Rate * 4) / 100
Multiplying both sides by 100 and dividing by 20,000 * 4, we get:
Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%
Therefore, the interest rate for the savings account is 5%.
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solve this algebra 1/4-2
Answer:
Step-by-step explanation:
Change 2 to 2/1, then multiply the top and bottom by 4 so it has the same denomiator as the 1/4.
\(\frac{1}{4} -\frac{8}{4} =-\frac{7}{4}\)
Answer:
-1 3/4
Step-by-step explanation:
Make the denominator the same
2 = 8/4
1/4 - 8/4 = -7/4 (mixed number: -1 3/4)
What is the slope of the linear function
y= -1/3x+1
is it
-1/3
1/3
-1
1
Answer:
-1/3
Step-by-step explanation:
This equation is in y-intersept form; y=mx+b, where m is the slope
Answer:
-1/3
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
the length of the garden should be 15 feet longer than its width and the area is less than 100 ft^2
Answer:
If the perimeter is 200feet (two lengths and two widths) then one width+one length equals 100feet.
If the length is 10 feet longer than the width, then length = 55 feet, and width =45 feet
Therefore the area of the rectangle is 45x55 feet, which equals 2475 sq.ft
Step-by-step explanation:
Hi! Nice to meet you and have a great day
Answer:
If the perimeter is 200feet (two lengths and two widths) then one width+one length equals 100feet.
If the length is 10 feet longer than the width, then length = 55 feet, and width =45 feet
Therefore the area of the rectangle is 45x55 feet, which equals 2475 sq.ft
WARM UP: Graph the coordinates of the triangle in the coordinate plane. Multiply each coordinate by a scale factor of 3 (k=3). Then, graph the new triangle.
The two triangles are similar triangles and the graph of the triangles are attached
Graph the coordinates of the triangle in the coordinate plane.The coordinates of the triangle are given as
A (0, 3), B (3, 3) and C (3, -1)
So, we enter the above coordinates in a graphing calculator
See attachment for the graph of the triangle
Multiply each coordinate by a scale factor of 3 (k=3).
Here, we have
A' 3 * (0, 3), B' 3 * (3, 3) and C' 3 * (3, -1)
This gives
A' (0, 9), B' (9, 9) and C' (9, -3)
Next, we enter the above coordinates in a graphing calculator
See attachment for the graph of the triangle
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Which phrase should be inserted on the line to make a true statement? Use the models to help.
Answer:
2/3 = 8/12
Step-by-step explanation:
2/3 vs 8/12
Multiply the left by 4/4 to get common denominators
2/3 *4/4 = 8/12
They are equal
Answer:
is equal to or awnser D
Step-by-step explanation:If you divide the you get the same awnser
10. How many solutions does this system of equations have? Explain how you know.
y=-4x+3
2x+8y=10
Answer:
One solution
Step-by-step explanation:
If you graph this you will see the lines intersect once.
Solve for x:
10 = x+25
Answer:
\(\boxed{\sf x=-15}\)
Step-by-step explanation:
\(\sf 10=x+25\)
\(\sf x+25=10\)
\(\boxed{\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}}\)
\(\sf x+25-25=10-25\)\(\sf x=-15\)Answer:
x = -15
Step-by-step explanation:
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Mrs. Robinson surveyed her class about what flavor cake and ice cream they wanted for their class party. The results were split evenly between the cake with 15 choosing chocolate cake and 15 choosing yellow cake. Of the students who chose chocolate cake, 12 also chose vanilla ice cream. There were 7 students in all that chose strawberry ice cream. Construct a two -way table summarizing the data
Answer:
Answer would be 12
Step-by-step explanation:
i'm not always accurate but your welcome!
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A cone with height h and radius r has volume V = 13πr2h. If a certain cone with a height of 9 inches has volume V = 3πx2 + 42πx + 147π, what is the cone’s radius r in terms of x?
ANALYZING DATA The table shows the daily changes in the value of a stock over 12 days.
Changes in Stock Value (dollars)
2.03
-13.78 -2.41
0.67
-0.28
1.05
2.64
0.66
4.02
-3.01
1.39
2.20
a. Find the mean, median, and mode of the changes in stock value. Round to the nearest thousandth if necessary.
The mean of the stock is 0.385 and the median is 0.665
Given data ,
To find the mean, median, and mode of the changes in stock value, we can use the following steps:
Sort the changes in stock value in ascending order:
-13.78, -3.01, -2.41, -0.28, 0.67, 0.66, 1.05, 1.39, 2.03, 2.20, 2.64, 4.02
Now , to calculate the mean:
Mean = (sum of all values) / (number of values)
Mean = (-13.78 - 3.01 - 2.41 - 0.28 + 0.67 + 0.66 + 1.05 + 1.39 + 2.03 + 2.20 + 2.64 + 4.02) / 12
Mean ≈ 0.385
Now , to calculate the median:
Since we have 12 values, the median will be the average of the 6th and 7th values in the sorted list.
Median = (0.67 + 0.66) / 2
Median ≈ 0.665
Now , to calculate the mode:
The mode is the value that appears most frequently in the list. In this case, there is no value that appears more than once, so there is no mode.
Hence , the mean is approximately 0.385, the median is approximately 0.665, and there is no mode in the list of changes in stock value
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