Answer:D
Step-by-step explanation:
What is the solution to the equation 3 square root 5x-4 = 3 square root7x+8?
The following graph portrays the distribution of the number of spicy chicken sandwiches sold at a nearby Wendy's for the last 141 days.
The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67. (Round your answers to 2 decimal places.)
If we use the Empirical Rule, on 68 percent of the days sales will be between
95 percent of the days sales will be between
68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.
What is the empirical rule?If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.
We have:
The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67.
As we know, from the empirical rule, 68% of the data will lie in one standard deviation of the mean, i.e., in the interval with the endpoints x±s
for samples and with endpoints u±б for the population.
x = 91.9
s = 4.67
x - s = 91.9 - 4.67 = 87.23
x + s = 91.9 + 4.67 = 96.57
68% of the day's sales will be between 87.23 and 96.57
95% of the data will lie within two standard deviations of the mean, which means in the interval with the endpoints x±2s for samples and with endpoints u±б population.
x - 2s = 82.56
x + 2s = 101.24
On 95% of the days, sales will be between 82.56 and 101.24
Thus, 68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.
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Enter the correct answer in the box.
Function g has the same a value as function f, but its vertex is 2 units below and 3 units to the left.
f(x) = x² - 4x - 32
Write the vertex form of the equation modeling function g.
The equation in the vertex form of g(x) is:
[tex]g(x) = (x + 1)^2 - 38[/tex]
How to get the equation of function g?
We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).
So first, let's rewrite f(x) to its vertex form:
[tex]f(x) = x^2 - 4x - 32[/tex]
The vertex is at:
[tex]x = -(-4)/2*1 = 2[/tex]
The y-value of the vertex is:
[tex]f(2) = 2^2 - 4*2 - 32 = -36[/tex]
Then the vertex form of f(x) is:
[tex]f(x) = (x - 2)^2 - 36[/tex]
If we move this vertex 2 units below, and 3 units to the left, then we have:
[tex]g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38[/tex]
That is the equation for g(x) in vertex form.
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An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that average refers to
following claims must be true based on this information?
Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.
Last year at least one of their clients made a profit of
exactly 10%.
Two years ago some of their clients made a profit of at least
10%.
Last year some of their clients made a profit of
0
10% or more.
O
O Last year all of their clients made a profit of more than 2%.
Last year, the number of their clients who made a profit of
10% or less was equal to the number of their clients who
made a profit of 10% or more.
The statements that are true based on the information are:
1. Last year at least one of their clients made a profit of exactly 10%.
3. Last year some of their clients made a profit of 10% or more.
Options 1 and 3 are the correct answer.
We have,
1. Last year at least one of their clients made a profit of exactly 10%.
- True.
The investment company advertised that, on average, their clients made a profit of 10%.
This means there must be some clients who made exactly 10% profit.
2. Two years ago some of their clients made a profit of at least 10%.
Not enough information is given to determine the accuracy of this statement.
The information provided only refers to last year's profits, not profits from two years ago.
3. Last year some of their clients made a profit of 10% or more.
- True.
The average profit of the clients was 10%, indicating that some clients made a profit of 10% or more.
4. Last year all of their clients made a profit of more than 2%.
- Not necessarily true.
The average profit was 10%, but this does not guarantee that all clients made a profit greater than 2%.
Some clients might have made less than 2% or even incurred losses.
5. Last year, the number of their clients who made a profit of 10% or less was equal to the number of their clients who made a profit of 10% or more.
- Not enough information is given to determine the accuracy of this statement.
The average profit of 10% does not tell us about the distribution of profits among clients to make this comparison.
Thus,
The statements that are true based on the information are:
1. Last year at least one of their clients made a profit of exactly 10%.
3. Last year some of their clients made a profit of 10% or more.
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In 2005 , a study at Blinn College was conducted to determine whether a relationship exists between a student who eats breakfast and his or her Biology grade. The study examined 1259 college students on a specific biology test. The accompanying tables show the relative frequency, by grade, of the 825 students who did eat breakfast and the 434 who did not eat breakfast on the morning of the test.
Students who did not eat breakfast
Grade Relative frequency
A 0.10
B 0.19
C 0.22
D 0.17
F 0.32
Students who ate breakfast
Grade Relative frequency
A 0.18
B 0.38
C 0.17
D 0.14
F 0.14
Select the statements that are accurate regarding the given data sets.
Eating breakfast ensures that a student will pass an exam.
The data show that skipping breakfast is associated with earning lower exam grades.
There is an increase in B's for those who do eat breakfast before the exam.
The data shows that skipping breakfast is not associated with earning lower grades.
Students are more likely to earn an A on an exam if they do not eat breakfast.
Answer:
1. The data show that skipping breakfast is associated with earning lower exam grades.
2. There is an increase in B's for those who do eat breakfast before the exam.
A chain weighs 12 pounds per foot. How many ounces will 7 inches weigh?
Answer:
The chain of the length 7 inches weighs 112 ounces.
Step-by-step explanation:
As we know there are 12 inches in a foot and 16 ounces in a pound
That is 1 foot = 12 inches.
and 1 pound = 16 ounces.
Given that the weight of the chain that is 1 foot long = 12 pounds
So weight of the chain per inch is = 12/12
which is equal to 1 pound
and according to the formula 1 pound = 16 ounces
So weight of the chain per inch is = 16 ounces
therefore weight of the chain that is 7 inch long = 7 × 16
that is 112 ounces.
The chain of the length 7 inches weighs 112 ounces.
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on a day in winnipeg with 10 1/2 h of daylight, it was sunny for 1/3 of that time. for how many hours was it sunny that day
Considering the multiplication of mixed fractions, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.
Multiplication of mixed fractionsTo multiply mixed fractions, it is necessary to transform these fractions into improper fractions. To do this, the whole part is multiplied by the denominator of the fraction that accompanies it. The result of the multiplication is added to the numerator of the fraction that accompanies it, and it will be the denominator of the new fraction, while the denominator remains the same.
After transforming the mixed fractions to be multiplied into improper fractions, they are multiplied. To do this, it is necessary to multiply the numerators of the two fractions, and the denominators of the fractions. If the resulting product needs to be simplified to lowest terms, divide the numerator and denominator by common factors.
Sunny hoursOn a day in winnipeg with 10[tex]\frac{1}{2}[/tex] h of daylight, it was sunny for [tex]\frac{1}{3}[/tex] of that time. This is:
10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex]
Solving:
10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex] = [tex]\frac{10x2+1}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{21}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{21x1}{2x3}[/tex]= [tex]\frac{21}{6}[/tex]= 3.5
Finally, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.
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Which graph best represents the equation shown below? 3x + y = 2 A. B. C. D.
Answer:
The plots are (0,2) (1,-1)
Step-by-step explanation:
a slanted line starting from top left corner ending in the bottom right
solve for x
[tex]\bold{x {}^{2} + 5x + 6 = 0}[/tex]
ty! ~
Answer:
x = -2x = -3Step-by-step explanation:
[tex] \bf {x}^{2} + 5x + 6 = 0[/tex]
Write the equation in factored form.
[tex]\bf (x + 2)(x + 3) = 0[/tex]
Separate equations, and set each factor to zero.
[tex]\bf x + 2 = 0[/tex]
[tex]\bf x + 3 = 0[/tex]
Rearrange and isolate the variable to find the solutions
[tex]\bf x = - 2[/tex]
[tex]\bf x = - 3[/tex]
------------------------------------
Answer:
x=-3 x=-2
Step-by-step explanation:
x^2 +5x+6 =0
We need to factor the equation
What two numbers multiply to 6 and add to 5
3*2 = 6
3+2 =5
(x+3)(x+2)
Using the zero product property
x+3 =0 x+2 =0
x=-3 x=-2
A recipe calls for 4 cups of peanuts for 5 cups of flour. Using the same recipe, how many cups of flour will you need for 3 cups of peanuts
I really need help
Find the critical point for f(x)=x^2-2x+4 and determine their nature.
Select one:
O a. (3, 1) minimum point
O b. (1, 3) minimum point
O c. (1, 3) maximum point
O d. (3, 1) maximum point
For the regions bounded by y = 6cosx and y = one fourth x squared minus 7.
Part A: Find the limits of integration. (10 points)
Part B: Write the expression representing the total area. (10 points)
Part C: Solve for the total area. (10 points)
For the regions bounded by y = 6cosx and y = one-fourth x squared minus 7, the limits of integration, the expression representing the total area, and the total area are mathematically given as
A=27.03squnit
What are the limits of integration, the expression representing the total area, and the total area.?
Generally, the equation for expression is mathematically given as
y = 6cosx
y=(1/4)x^2-7
therefore
[tex]A=\int^{b}_a (f(x)-g(x))dx[/tex]
The limits are
a=0 b=2\pi
Hence
[tex]A=\int ^{2\pi}_0 (6cosx -((1/4)x^2-7))dx\\\\solving\\\\A=\int^{2\pi}_0 (6cosx -((1/4)x^2-7))dx[/tex]
A=27.03squnit
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HELP! ASAP!
A box without a top is to be made from a rectangular piece of cardboard, with dimensions 4 in. by 8 in., by cutting out square corners with side length x and folding up the sides.
(a) Write an equation for the volume V of the box in terms of x.
(b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Step-by-step explanation:
Part A:
So the height is going to be x when you fold the sides up. So that's one part of the volume but for the width it was going to be 4 but since two corners were cut out with the length x the new width is going to be (4-2x). The same thing applies for the length which should be 8 inches but since two corners were removed with the length x it's now (8-2x)
v = x(4-2x)(8-2x)
Part B:
The volume can be graphed although there must be a domain restriction since the height, width, or length cannot be negative. So let's look at each part of the equation
so for the x in front it must be greater than 0 to make sense
for the (4-2x), the x must be less than 2 or else the width is negative.
for the (8-2x) the x must be less than 4 or else the length is negative
so the domain is going to be restricted to 0 < x < 2 so all the dimensions are greater than 0
By using a graphing calculator you can see the maximum of the given equation with the domain restrictions is 0.845 which gives a volume of 12.317
$10,000 is invested for 4 years at an annual simple interest rate of 16%.
Answer:
$16,400
Step-by-step Explanation:
Step 1: We multiply $10,000 by 16%, getting $1,600.
Step 2: We then multiply $1,600 by 4 (which is given). That gives us $6,400.
Step 3: Add that to $10,000. We get $16,400 as the answer!
Please mark me as brainliest! I really need it!!! Thanks!Answer:
Simple interest = P x r x t
= 10,000 x 16/100 x 4
= $6400
Final amount = P (1 +rt)
= 10,000 (1 + 16/100 x 4)
= $16400
(or you can just add the simple interest to the principle amount to get the final amount)
Question 15 (06.01 LC)
Classify the expression: 5x³ - 4x²
Quadratic expression
Linear expression
Cubic expression
Constant expression
Answer:
Cubic expression
Step-by-step explanation:
Polynomials with a degree of 3 are known as cubics.
Answer:
cubic expression
Step-by-step explanation:
it is cubic when raised to the power of 3
transform each graph below.
(a) The graph of y=f(x) is shown. Draw the graph of y= f(2x).
(b) The graph of y=g (x) is shown. Draw the graph of y=1/2g(x).
Answer:
Step-by-step explanation:
Evaluate 3a-5b when a=-3 and b=-2
Answer: 1
Step-by-step explanation:
Substituting in the given values,
3a-5b=3(-3)-5(-2)=-9+10=
How do I solve for x?
Answer:
3
Step-by-step explanation:
1: Turn the mixed fraction into improper.
2: Multiply 3/5 to each side
3: The you get x = 3
You need to multiply the fraction instead of division because multiplying by the reciprocal is the same as dividing the normal fraction.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5 = 1\dfrac{2}{3}x}[/tex]
[tex]\mathsf{1\dfrac{2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{1\times3 + 2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{3 + 2}{3}x = 5}[/tex]
[tex]\mathsf{\dfrac{5}{3}x = 5}[/tex]
[tex]\large\textbf{MULTIPLY }\rm{\bf \dfrac{3}{5}}\large\textbf{ to BOTH SIDES}[/tex]
[tex]\mathsf{{\dfrac{3}{5}\times\dfrac{5}{3}x= \dfrac{3}{5}\times 5}}[/tex]
[tex]\large\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{x = \dfrac{3}{5}\times5}[/tex]
[tex]\mathsf{x = \dfrac{3}{5}\times\dfrac{5}{1}}[/tex]
[tex]\mathsf{x = \dfrac{3\times5}{5\times1}}[/tex]
[tex]\mathsf{x = \dfrac{15}{5}}[/tex]
[tex]\mathsf{x = 15\div5}[/tex]
[tex]\mathsf{x = 3}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Math: Surface Area word problem..10 pts for your help!
The formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]
How to determine the surface area?We have:
[tex]S(r) = 4\pi r^2[/tex]
Also, we have:
[tex]P(t) = \frac 43t[/tex]
The above can be rewritten as:
[tex]r = \frac 43t[/tex]
Substitute [tex]r = \frac 43t[/tex] in S(r) to determine the function N(t)
[tex]S(r) = 4\pi (\frac 43t)^2[/tex]
Express as N(t)
[tex]N(t) = 4\pi (\frac 43t)^2[/tex]
Expand the exponent
[tex]N(t) = 4\pi *\frac {16}9t^2[/tex]
Evaluate the product
[tex]N(t) = \frac {64}9\pi t^2[/tex]
Hence, the formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]
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Jessie bought a vacuum cleaner priced at $79 with a 6% sales tax rate. What is the total cost of the vacuum cleaner after-
tax?
Answer:
83.74
Step-by-step explanation:
First find the amount of the tax
79 * .06
4.74
Add this to the original price
79+4.74
83.74
Suppose we want to choose 2 colors, without replacement, from the 3 colors red, blue, and green . How many ways can this be done, if the order of choices is relevant
The 2 colors can be chosen in 6 different ways.
In how many ways can the colors be chosen?Here we need to identify the selections and the numbers of options for each.
Here the selections are:
Color 1.Color 2.And the numbers of options for each are:
Color 1: 3 options (there are 3 colors).color 2: 2 options (one is already taken).The total number of combinations is:
C = 3*2 = 6
The 2 colors can be chosen in 6 different ways.
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HELP ME PLEASE
13
25
Which expression represents the volume, in cubic units,
of the composite figure?
○ π(57)(13) —π (5²)(12)
○ π(5²)(13) — π (5²)(25)
○ ~(5²)(13) + = π (5²)(12)
○pi(5²)(13) + = π (5²³)(25)
Answer:
π(5²)(13)+⅓π(5²)(12)
Step-by-step explanation:
You can find the volume of the cylinder by:
V=πr²h
which is V1=π(5²)(13)
and the volume of the crooked cone by:
⅓πr²h
which is V2=⅓π(5²)(12)
and you need the volume of the whole shape. you can find by adding V1+V2
determining height from a shadow measuring 88 meter
Answer:
Height = 132 mt
Step-by-step explanation:
Shadow lengths are proportional to the height of the object.
So, multiply the length of the tree's shadow by your height.
If you are 5 feet (1.5 meters) tall, and the length of shadow is 88 meters long,
Multiply them together: 1.5 x 88 = 132 mt.
Hence, Height = 132 mt.
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determine domain and range from graph
Domain: (-∞,∞)
Range: (-∞,-3]
Step-by-step explanation:
A quadratic equation graphs a parabola. Therefore there will be arrows on the bottom of the graph as it will go down forever. The domain (min x-values to max x-values) is
(-∞,∞) because the graph keeps on going down and to the right and left. The range (min y-values to max y-values) is (-∞,-3] because the lowest y-value the graph goes to is -∞ nd the highest y-value is -3.
A satellite orbits the Earth with an elliptical orbit modeled by x squared over 43 million eight hundred twenty four thousand four hundred plus y squared over forty seven million one hundred ninety six thousand nine hundred equals 1 comma where the distances are measured in km. The Earth shares the same center as the orbit. If the radius of the Earth is 6,370 km, what is the maximum distance between the satellite and the Earth?
250 km
500 km
6,620 km
6,870 km
"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is
D= 510 km. Option B. This is further explained below.
What is Kepler Orbit?Generally, In the study of astrodynamics, an ellipse of the satellite is often referred to as a Kepler Orbit
The function of the elliptical orbit is
[tex]\frac{(x-h)^2}{a^2}+\frac{(x-k)^2}{b^2}=1[/tex]
compared to
[tex]\frac{(x^2)^2}{47334400}+\frac{(y^2)^2}{43956900}=1[/tex]
Hence
a = √(47,334,400 km²)
a= 6,880 km.
In conclusion, The distance of the satellite above the Earth's surface.
D = a - r
D= 6,880 km - 6,370 km
D= 510 km
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"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is D= 510 km. Option B.
What is Elliptical Orbit?An elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0.
The function of the elliptical orbit is
[tex]\frac{{(x-h)}^2}{a^2}+ \frac{{(y-k)}^2}{b^2} = 1[/tex]
compared to
√([tex]\frac{({x^2)}^2}{47,334,400} + \frac{({y^2)}^2}{43956900} = 1[/tex]
a = √(47,334,400 km²)
a= 6,880 km.
Now,
D = a - r
D= 6,880 km - 6,370 km
D= 510 km
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(08.01 MC)
Find the height of a square pyramid that has a volume of 75 cubic feet and a base length of 5 feet.
A. 5 feet
B. 9 feet
C. 25 feet
D. 45 feet
Answer:
A. 5 feet
Step-by-step explanation:
A triangle has two sides of lengths 4 and 15. What value could the length of
the third side be? Check all that apply.
A. 19
B. 11
C. 4
OD. 15
OE. 12
F. 13
The value could the length of the third side will be 11,12,13,15. Options B, D, E, and F are the correct answers.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
According to the triangle Inequality theorem, any two triangle sides must add up to more than the third side's length.
You may get the potential length of a triangle by multiplying the sum of two sides by the difference between two sides.
Therefore,
Let x is the possible length of the third side of a triangle.
14-4<x<15+4
10<x<19
The values of the third side is lies between the 10 and 19.The value could the length of the third side will be 11,12,13,15
Hence, options B, D, E, and F are the correct answers.
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Find the formula for the area of the shaded region in the figure.
x² = 4py
ہے
The formula for the area of the shaded region in the figure.
x² = 4py is mathematically given as
[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]
What is the formula for the area of the shaded region in the figure?Parameters
[tex]$x^{2}=4 p y$[/tex]
[tex]$y=h$[/tex]
[tex]\therefore x^{2}=4 p h \Rightarrow x=2 \sqrt{p h} \\[/tex]
Generally, the equation for the Area is mathematically given as
[tex]& A=2 \int_{0}^{2 \sqrt{p h}}\left(h-\frac{x^{2}}{4 p}\right) d x \\\\& A=2\left(h x-\frac{x^{3}}{12 p}\right]_{0}^{2 \sqrt{p h}} \\\\& A=2\left[\left[h 2 \sqrt{p h}-\frac{1}{12 p} \cdot(2 \sqrt{p h})^{3}-0\right]\right. \\[/tex]
[tex]&A=2\left[2 h^{3 / 2} \sqrt{p}-\frac{8(\sqrt{p})^{3}(\sqrt{h})^{3}}{12 p}-0\right] \\\\&A=2\left[2 h^{k / 2} \sqrt{p}-\frac{2}{3} \sqrt{p} \cdot h^{3 / 2}\right] \\\\&A=2 \times \frac{4 \sqrt{p} \cdot h^{3 / 2}}{3} \\\\&A=\frac{8}{3} \cdot \sqrt{p} \cdot \sqrt{h} \cdot h \\\\&A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]
[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]
In conclusion, the equation for the Area is
[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]
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the value of a savings account can be found using the equation 300(1.03)^24. the interest is compounded monthly.
the interest rate is _____ per year
a. 12%
b. 0.25%
c. 36%
d. 1.5%
The interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have:
The value of a savings account can be found using the equation =
= 300(1.03)²⁴
From the function:
F(x) = a(1+r)ˣ
On compare:
1 + r = 1.03
r = 0.03
or
r = 3% monthly
r = 3×12 = 36% yearly
Thus, the interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.
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answer the following function, algebra 1.
Answer:
g(f(x)) = 1x² + 1
Step-by-step explanation:
We are given:
f(x) = x² - 1
g(x) = x + 2
And we want to find g(f(x)).
To do this, we substitute f(x) as x in x+2 (the expression that is equal to g(x)), as g(f(x)) is saying that f(x) is the value of x in g(x).
So, this will be:
g(f(x)) = x² - 1 + 2
Simplify
g(f(x)) = x² + 1
In your system, place 1 in front of x² - this is the coefficient of x², and also 1 after that - this is a constant.
