Hence the correct answer is Option (A) i.e. 37
What is Composition of a Function?The composition of a function is an operation where two functions say f and g generate a new function.
How to Solve:Given,
[tex]f(x)= x^2+1[/tex]-------------------(1)
and, [tex]g(x)= x-4[/tex]
Now ,
[tex]fog(x)=f[g(x)][/tex]
[tex]=f(x-4)[/tex]
[tex]=(x-4)^2+1[/tex] (from 1)
[tex]=x^2-8x+16[/tex][tex]+1[/tex]
[tex]fog(x)=x^2-8x+17[/tex]-----------------(2)
Now , we need to find [tex]fog(10)[/tex]
so, put x=10 in equation 2, we get:
[tex]fog(10) = 10^2 -8(10)+17\\fog(10) = 100-80+17\\fog(10) = 37[/tex]
Hence, the answer is 37
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If one quart bottles of apple juice have weights that are normally distributed with a mean of 64 ounces and a standard deviation of 3 ounces, what percent of bottles would be expected to have less than 58 ounces?
(1) 6.7% (3) 0.6%
(2) 15.0% (4) 2.3%
Answer:
Approximately 2.5%
Step-by-step explanation:
Note that if the mean is 64 oz, then one standard deviation below that would be 61 oz., and two standard deviations beow 64 oz would be 58 oz.
So our task boils down to finding the area under a standard normal curve to the left of 58 oz.
We can do this in two ways.
One is to apply the Empirical Rule, which states that 95% of data lies within 2 standard deviations of the mean, on both sides of the mean. Thus, 5% lies outside the lines representing 2 standard deviations on both sides; half of that (representing the area under the curve to the left of 58) is 2.5%, which is the answer to this question.
The other way is to use a calculator with probability distribution functions built in:
normcdf(-1000, 58, 64, 3) = 0.0228, or approximately 2.28%. Here "-1000,58" represents the area under the curve to the left of 58, 64 represents the mean, and 3 represents the standard deviation.
1050 households in the town how many own a dog
Answer:
357 dogs
Step-by-step explanation:
50 households are randomly selected f r om the town 17 own a dog
17/50 x 100 = 34%
1050 x 34% = 257
1. Find 1% of a number: a) 400
b) 2,500
c) 657
d) 12
Step-by-step explanation:
[tex]a) \: 1\% \: of \: 400 = \frac{1}{100} \times 400 = 4 \\ \\ b) \: 1\% \: of \: 2500 = \frac{1}{100} \times 2500 = 25 \\ \\ c) \: 1\% \: of \: 657= \frac{1}{100} \times 657 = 6.57 \\ \\ d) \: 1\% \: of \: 12= \frac{1}{100} \times 12 = 0.12 \\ [/tex]
(Day 8) Find the value of each variable. The dot represents
the center.
a =
b=
C=
Answer:
Step-by-step explanation:
a=180-122=58°
Let ABC be the triangle in which BC is diameter.
Diameter always make angle 90° on the circumference.
so b=90°
∠B=1/2×58=29°
29+b+c=180
29+90+c=180
c=180-119=61°
Daily attendance at the water park: 346, 250, 433, 369, 422, 298
Answer:
353
Step-by-step explanation:
250+298+346+369+422+433=2,118
2,118/6=353
Freddie uses 14 cup of blueberries for a batch of pancakes.
Drag the correct equation next to the number of cups to show how many batches of pancakes he can make from that number.
Answer:
Where are the equations
Step-by-step explanation:
Check the functions whose inverses are also functions
The functions whose inverses are also functions are
b. On a coordinate plane, an exponential functions increases from quadrant 2 into quadrant 1.c. On a coordinate plane, a cubic function has an x-intercept of (0, 0).Checking the functions whose inverses are also functions.From the question, we have the following parameters that can be used in our computation:
The list of options
Analyzing each statement, we have
a. On a coordinate plane, an absolute value function opens down.
The absolute value function f(x)=∣x∣ does not have an inverse that is a function because it fails the horizontal line test.
Specifically, any horizontal line intersects the graph of the absolute value function at most twice.
So, its inverse is not a function.
b. On a coordinate plane, an exponential function increases from quadrant 2 into quadrant 1.
Exponential functions, such as
f(x) = eˣ or f(x) = abˣ, do have inverses that are functions.
They pass the horizontal line test, and their inverses are logarithmic functions.
c. On a coordinate plane, a cubic function has an x-intercept of (0, 0).
A cubic function, such as f(x) = x³, does have an inverse that is a function.
The cubic function has an x-intercept at (0, 0), and its inverse is a cubic root function.
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Question
Check the functions whose inverses are also functions.
a. On a coordinate plane, an absolute value function opens down.
b. On a coordinate plane, an exponential functions increases from quadrant 2 into quadrant 1.
c. On a coordinate plane, a cubic function has an x-intercept of (0, 0).
what 2 numbers multiply to -4 and add to -8
Answer: 8
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
AB is a diameter of circle S. Which arc must be a minor arc?
ZW
AWB
AB
WBZ
please help
There are 14 books on a shelf. 6 of these books are new.
(a) What is the ratio of used books to all books?
(b) What is the ratio of new books to used books?
Answer:
6:14
Step-by-step explanation:
What percent of Troy's gross pay is his net pay?
What is the area of a triangle that has a base of 15 yards and a height of 11 yards?
please help :)
165 yd2 82.5 yd2 41.25 yd2 330 yd2
Answer:
82.5
Step-by-step explanation:
The formula for the area of triangle is 1/2 B * H
1/2 of the base is 7.5
multiply that by 11
and you get
82.5
Pls help I need an answer soon and pls make sure it’s right
Answer:
34
Step-by-step explanation:
4x+3x-8=90
so lets start by solving this
Let's solve your equation step-by-step.
4x+3x−8=90
Step 1: Simplify both sides of the equation.
4x+3x−8=90
4x+3x+−8=90
(4x+3x)+(−8)=90(Combine Like Terms)
7x+−8=90
7x−8=90
Step 2: Add 8 to both sides.
7x−8+8=90+8
7x=98
Step 3: Divide both sides by 7.
7x
7
=
98
7
x=14
Answer:
x=14
so plug this in and you get 3*14 -8
this equals 34
brainliest?
Answer:
It is 34 degrees
Step-by-step explanation:
Step 1: Make an equation
[tex]4x + 3x - 8 = 90[/tex]
Step 2: Combine like terms
[tex](4x + 3x) - 8 = 90[/tex]
[tex]7x - 8 = 90[/tex]
Step 3: Add 8 to both sides
[tex]7x - 8 + 8 = 90 + 8[/tex]
[tex]7x = 98[/tex]
Step 4: Divide both sides by 7
[tex]7x / 7 = 98 / 7[/tex]
[tex]x = 14[/tex]
Step 5: Find the measure
[tex]3x - 8[/tex]
[tex]3(14) - 8[/tex]
[tex]42 - 8[/tex]
[tex]34^o[/tex]
Answer: It is 34 degrees
Which graph best represents the solution to the system of equations shown below? y = -4x - 19 y = 2x − 1 A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 7, 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 3, 7. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, negative 7. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 7, negative 3.
Answer:
Option 3
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, negative 7.
Step-by-step explanation:
y = -4x - 19 y = 2x − 1
-4x - 19 = 2x - 1
6x = -18
x = -3
y = 2(-3) - 1 = -7
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, negative 7.
What is a system of equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought
Given
y = -4x - 19 y = 2x − 1
-4x - 19 = 2x - 1
6x = -18
x = -3
y = 2(-3) - 1 = -7
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Victoria wants to estimate the mean weight of apples in her orchard. She'll sample n apples and make a 95%
confidence interval for the mean weight. She is willing to use 0 = 15 grams as an estimate of the standard
deviation, and she wants the margin of error to be no more than 5 grams.
Which of these is the smallest approximate sample size required to obtain the desired margin of error?
The smallest approximate sample size required for Victoria to estimate the mean weight of apples with a 95% confidence level and a margin of error of no more than 5 grams is 35 apples.
Victoria wants to estimate the mean weight of apples in her orchard with a 95% confidence interval and a margin of error of no more than 5 grams, using an estimated standard deviation of 15 grams. To determine the smallest sample size (n) required, the following formula which incorporates the z-score for the desired confidence level, the standard deviation, and the desired margin of error can be used:
n = (z * σ / E)^2,
where z is the z-score corresponding to a 95% confidence level (which is 1.96), σ (sigma) is the estimated standard deviation (15 grams), and E is the desired margin of error (5 grams).
Plugging the values in gives us: n = (1.96 * 15 / 5)^2 = (1.96 * 3)^2
= 5.88^2 = 34.5744.
Since we cannot have a fraction of an apple, we round up to the nearest whole number. Therefore, the smallest approximate sample size required is 35 apples.
Victoria needs a sample size of at least 35 apples.
Victoria wants to estimate the mean weight of apples in her orchard with a 95% confidence interval and a margin of error no more than 5 grams. We are given the standard deviation of 15 grams.
To find the smallest approximate sample size n, we can use the formula for margin of error (E) in a confidence interval:
E = Z * (σ/√n)
Here, Z is the Z-score for a 95% confidence level, which is 1.96, σ (sigma) is the population standard deviation (15 grams), and n is the sample size.
Rearrange the formula to solve for n:
n = (Z * σ / E)²
Substitute the given values:
Z = 1.96σ = 15 gramsE = 5 gramsCalculate:
n = (1.96 * 15 / 5)²
n = (1.96 * 3)²
n = (5.88)²
n ≈ 34.57
Since the sample size must be a whole number, we round up to the nearest whole number, which is 35. Therefore, Victoria needs a sample size of at least 35 apples to achieve her desired margin of error.
Mark and John were sharing the $10 cost to rent some video games with another friend. Mark paid $3, John paid 2/5 of the total, and their friend paid the rest.
Well im quessing the question is how much did someone pay so im gonna tell you john paid 4 dollars because 1/5 of ten is 2 so 2/5 is ten meaning the extra friend payed $3
Help me thank you 16 points!
Answer:
-64000
Step-by-step explanation:
Work your way upwords. The number next to the 2 would be -5. This makes the number above the 2 -10. Multiplying it out to the top gets you -64,000
The top block would equal -64000 once you have put all the numbers in every block.
Consider the following graph, which details the observed bear population in two national parks. A graph titled Bears Observed in Park has month on the y-axis and number of bears observed on the y-axis, going from 37 to 53. In the same month, there are 2 points marked on the graph. All points are connected by overlapping lines. Of the following, which option or options would help make this graph less misleading? I. The scale on the x-axis should be resized. II. The scale on the y-axis should be resized. III. The identity of the two parks should be more clearly differentiated. a. I and II b. II and III c. III only d. I and III
ANSWER IS B
Answer:
b. II and III
Step-by-step explanation:
A graph is a data presentation that has two axis - x and y, divided into appropriate scales.
A scale is used to divide given units into equal parts. It is crucial to and used to create uniformity in drawing of graphs. Choosing a good scale to represent an information on a graph is vital to avoid confusion. This can be done by considering the variations in the values forming the data.
In the question, the single graph shows an information about the bear population in two national parks. Thus, the scale of the y-axis must be adjusted and the identity of the two parks be more differentiated so as to make the graph less misleading.
Answer:
B
Step-by-step explanation:
Solve the system of equation
2x-y= 6
x+y= -3
that is the solution to the simultaneous equation
Answer:
(1, - 4 )
Step-by-step explanation:
Given the 2 equations
2x - y = 6 → (1)
x + y = - 3 → (2)
Adding the equations term by term will eliminate the term in y, that is
3x = 3 ( divide both sides by 3 )
x = 1
Substitute x = 1 into either of the 2 equations and solve for y
Substituting in (2) gives
1 + y = - 3 ( subtract 1 from both sides )
y = - 4
Solution is (1, - 4 )
Ratio that is equivalent to 8:20
Answer:
Step-by-step explanation:
25 is equivalent to 820 because 2 x 20 = 5 x 8 = 40. 410 is equivalent to 820because 4 x 20 = 10 x 8 = 80. 615 isequivalent to 820 because 6 x 20 = 15 x 8 = 120.
Answer:
4:10 = 8:20( when multiplied by 2)
24:60 divide by 3 we get 8:20
2:5 multiply by 4 we get 8:20
Five over twenty five÷ 100
Answer:
20
Step-by-step explanation:
According to the question,five over 25 divided by 100
Can also be written as
5/25/100
So
5/25×100
1/5 ×100
20
So the final answer is 20
Pls can someone answer this
Answer: they are parallel to each other plus they're both obtuse triangles
what is the square root of i?
i is an imaginary number.
I = square root -1
Find square root of i:
Let square root I = a + ib
I = (a+ ib)^2
I = a^2 + i^2b^2+ 2abi
I = a^2 -b^2 + 2abi
Square root I = +/- square root 2/2+ I square root 2/2
Plz help me out ASAP!!!!!
Answer:
540
Step-by-step explanation:
A trapezoid has an area of 30m^2. if all of its side lengths are tripled, what will its new area be
Answer:
270
Step-by-step explanation:
Because we do not know what the side lengths are, as long as they multiply to 30m^2, it's fine
For this question, let's just say the base is 5, and the height is 6. If we triple 5, we get 15, and if we triple 6, we get 18. 15*18=270
Now what if, the sides are not 5 and 6. Will the area still be the same? Let's find out.
10*3=30 so we can say for this answer, the base is 3, and the height is 10.
10 tripled is 30, and 3 tripled is 9. 30*9=270
So as we look at these 2 answers. we can conclude that the new area, no matter the side lengths, will be 270
Hope this helpes!
Please someone help with my math
Answer:
1: do half then 12 more
2: 6/8 or 3/4
3: 8 or 8/100
4: 6.45,6.76
5: 1(83/100)
6:75/100
7:???
8:????
Step-by-step explanation:
hope this helped
Four students drew graphs of a linear function. Which student drew a line with a slope of 3? Analise On a coordinate plane, a line goes through points (negative 3, 0) and (0, 1). Benito On a coordinate plane, a line goes through points (0, negative 1) and (1, 2). Charlie On a coordinate plane, a line goes through points (0, negative 3) and (0, 3). Dariya On a coordinate plane, a line goes through points (2, 3) and (3, 0).
Answer:
Benito
Step-by-step explanation:
https://brainly.com/question/15495979
Benito drew a line with a slope of 3. This is determined by using the slope formula and identifying the rate of change in the y coordinates with respect to the x coordinates for each line drawn by the different students.
Explanation:To find the slope of a line on a coordinate plane, we can use the slope formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line.
Analise's line goes through points (-3,0) and (0,1). The slope would be (1-0)/(0-(-3)) = 1/3.Benito's line goes through points (0, -1) and (1, 2). The slope is (2-(-1))/(1-0) = 3.Charlie's line is vertical, going through the points (0,-3) and (0,3). Vertical lines do not have a defined slope.Dariya's line passes through (2,3) and (3,0). The slope is (0-3)/(3-2) = -3.Therefore, the student who drew a line with a slope of 3 is Benito.
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The Bowden family is shopping for a new television. They are making their decision based on brand and size. The family has 20 possible outcomes for choosing a television. Which is a possible number of brands and sizes that the family has to choose from? 10 brands and 10 sizes 5 brands and 4 sizes 4 brands and 16 sizes 2 brands and 20 sizes
Yuki wants a display that shows the spread of data above and below the median.
What data display should Yuki use?
A. A dot plot is best for displaying the spread of data above and below the median, so Yuki should use a dot plot.
B. Dot plots and box plots are best for displaying the spread of data above and below the median. For these data, the median is too large and close to the maximum, so Yuki should use a dot plot.
C. A box plot is best for displaying the spread of data above and below the median, so Yuki should use a box plot.
D. A histogram is best for displaying the spread of data above and below the median, so Yuki should use a histogram.
Answer:
C. A box plot is best for displaying the spread of data above and below the median, so Yuki should use a box plot.
Step-by-step explanation:
Neither dot plot nor histogram shows the median of data, but box plot it does. Also, box plots show the how spread data is from minimum value to first quartile, from first quartile to median, from median to third quartile and from third quartile to maximum value.
(6x2 - 4x + 11) + ( 4 - x2 – 3x)
Answer:
5x^2-7x+15
Step-by-step explanation:
(6x^2 - 4x + 11) + ( 4 - x^2 – 3x)
Combine like terms
6x^2 - x^2 -4x -3x +11+4
5x^2 -7x +15