Answer:
9 years
Step-by-step explanation:
Find three consecutive even integers such that the square of the third is 60 more that the square of the second
Answer:
-4,4,16
Step-by-step explanation:
They are all even integers.
-4^2=16
4^2=16
16^2=256
the square of the third,16 is 256 which is more than the square of the second,4=16
The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
Let the three even consecutive integers are 2n-2, 2n and 2n + 2.
According to the question,
So,
(2n + 2)² = (2n)² - 60
4n² + 4 + 8n = 4n² -60
8n = -64
n = -8
That means, the integers are -18, -16 and -14.
Therefore, the required even integers are -18, -16 and -14.
To learn more about the integers;
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Integrate the following: ∫[tex]5x^4dx[/tex]
A. [tex]x^5+C[/tex]
B. [tex]x^5[/tex]
C. [tex]5x^5+C[/tex]
D. [tex]5x^5[/tex]
Answer:
A. [tex]x^5+C[/tex]
Step-by-step explanation:
This is a great question! The first thing we want to do here is to take the constant out of the expression, in this case 5. Doing so we would receive the following expression -
[tex]5\cdot \int \:x^4dx[/tex]
We can then apply the power rule " [tex]\int x^adx=\frac{x^{a+1}}{a+1}[/tex] ", where a = exponent ( in this case 4 ),
[tex]5\cdot \frac{x^{4+1}}{4+1}[/tex]
From now onward just simplify the expression as one would normally, and afterward add a constant ( C ) to the solution -
[tex]5\cdot \frac{x^{4+1}}{4+1}\\[/tex] - Add the exponents,
[tex]5\cdot \frac{x^{5}}{5}[/tex] - 5 & 5 cancel each other out,
[tex]x^5[/tex] - And now adding the constant we see that our solution is option a!
Answer:
Answer A
Step-by-step explanation:
Use the property of integrals. You now have [tex]5 x\int\limits\,x^{4}dx[/tex] where the first x next to the 5 stands for multiplication. Let's evaluate it. We get [tex]5 (\frac{x^{5} }{5})[/tex]. From here, we can simplify this into [tex]x^{5}[/tex]. Add the constant of integration, which will give you the answer of [tex]x^{5} + C[/tex].
For each function, determine if it intersects or is parallel to the line y=−1.5x. If it intersects the line, find the intersection point. y=0.5x−6
Answer: the intersection point is (2.4, -4.8)
Step-by-step explanation:
A) we have the function:
y = 0.5*x - 6.
First we want to know if this function intersects the line y´ = -1.5*x
Now, first we can recall that two lines are parallel only if the slope is the same for both lines, here we can see that the slopes are different, so the lines are not parallel, which means that the lines must intersect at some point.
Now, to find the intersection point we asumme y = y´ and want to find the value of x.
0.5*x - 6 = -1.5*x
(0.5 + 1.5)*x - 6 = 0
2.5*x = 6
x = 6/2.5 = 2.4
Now, we evaluate one of the functions in this value of x.
y = 0.5*2.4 - 6 = -4.8
So the intersection point is (2.4, -4.8)
An object is moving at a speed of 7300 inches every 3 seconds. Express this speed in miles per day.
Answer:
≈3318 miles per day....
Step-by-step explanation:
A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 275 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related? Vaccination Status Diseased Not Diseased Total Vaccinated 53 17 70 Not Vaccinated 62 143 205 Total 115 160 275
Answer:
Step-by-step explanation:
From the give information: A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 275 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?
Vaccination Status Diseased Not Diseased Total
Vaccinated 53 17 70
Not Vaccinated 62 143 205
Total 115 160 275
In this study, we have two variables ( Vaccination and diseases status ) The null and the alternative hypothesis can be stated as follows:
Null hypothesis: The two variables ( Vaccination and diseases status ) are independent
Alternative hypothesis : The two variables ( Vaccination and diseases status ) are dependent
The Chi-square test statistics can be computed as:
The Expected Values for the table can be calculated by using the formula:
[tex]E_i=\dfrac{row \ total \times column \ total}{grand \ total}[/tex]
Vaccination Status Diseased Not Diseased Total
Vaccinated 29.273 40.727 70
Not Vaccinated 85.727 119.273 205
Total 115 160 275
[tex]Chi - Square \ X^2 = \dfrac{(O_i-E_i)^2}{E_i}[/tex]
Vaccination Status Diseased Not Diseased Total
Vaccinated 19.232 13.823 33.055
Not Vaccinated 6.564 45.573 52.137
Total 25.796 59.396 85.192
Therefore;
the Chi-Square Test Statistics = 85.192
For this study; we two rows and two columns
Therefore, the degree of freedom = (rows-1) × (columns-1)
the degree of freedom = (2 - 1) × (2 - 1)
the degree of freedom = 1 × 1
the degree of freedom = 1
Using the level of significance of ∝ = 0.05 and degree of freedom = 1 for the chi-square test
The p-value for the test statistics = 0.00001
Decision rule: Since the P-value is lesser than the level of significance , therefore we reject the null hypothesis at the level of significance of 0.05
Conclusion:
We accept the alternative hypothesis and conclude that the two variables
(Vaccination and diseases status ) are dependent i.e the vaccination and disease status are related
If 5e^x=300, x
I need help fast
Answer:
ln(60)
Step-by-step explanation:
We have the equation [tex]5e^x=300[/tex]. We can divide both sides of the equation by 5, getting [tex]e^x=60[/tex]. Finally, we can take the natural log of both sides, getting that x is equal to [tex]\ln(60)[/tex].
slope=4/3 find the equation of the parallel line through (5,5)
Answer:
[tex]y=\frac{4}{3}x-1.75[/tex]
Step-by-step explanation:
If the slope of a line is 4/3,
and we wanna find the equation of a line that is parallel to it and crosses through (5,5).
So we already have the slope because the slope of 2 parallel lines are the same.
y = 4/3x
Look at the image below↓
So now we just need to find the y-intercept.
After some numbers we got,
[tex]y=\frac{4}{3}x-1.75[/tex]
Look at the other image below↓
Thus,
the equation of the parallel line is [tex]y=\frac{4}{3}x-1.75[/tex].
Hope this helps :)
Zoey wants to use her iPad throughout a 6-hour flight. Upon takeoff, she uses the iPad for 2 hoursand notices that the battery dropped by 25%, from 100% to 75%. How many total hours can Zoeyexpect from the iPad on a full battery charge?
Answer:
8 hours
Step-by-step explanation:
25%= 2 hrs
100%=8 hrs
brainliest plsssssssssssssssssssss
-zylynn
3/4 (1/2x - 12) + 4/5 HELP
Answer:
3/8x - 9 4/5
Step-by-step explanation:
Well we need to simplify the following expression,
[tex]\frac{3}{4} (\frac{1}{2}x - 12) + \frac{4}{5}[/tex]
So we need to distribute 3/4 to (1/2x - 12)
3/8x - 9 + 4/5
3/8x - 9 4/5
Thus,
the answer is 3/8x - 9 4/5.
Hope this helps :)
What is a3 if an=64(12)n−1
Answer:
[tex]\huge\boxed{a_3=9,216}[/tex]
Step-by-step explanation:
[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]
Determine whether the function below is an even function, an odd function, both, or neither.
f(x)=x^6 + 10x^4-11x^2+19
ОА.
neither even nor odd
OB.
odd function
Ос.
both even and odd
OD.
even function
Reset
Next
Answer:
Step-by-step explanation:
even function are symmetrical about the y axis or f(-x)=f(x)
odd function are symmetrical about the origin -f(-x)=f(x)
f(x)=x^6 + 10x^4-11x^2+19
f(-x)=(-x)^6+10(-x)^4+11(-x)^2+19=x^6 + 10x^4-11x^2+19
the function is even
Adam is going to cook a turkey for 14 people
Answer:
they divied the turkey into 14 pices
Step-by-step explanation:
PLEASEEEEE HELPPOO
For Individual or Group Explorations
Maximizing the Total Profit
Payles at The Christmas Store very periodically with a high ef 550.000 in December
the Christmas Stove also comes the Powe, where profits reach a high of $80,000
in Aurust and a few of $20,000 in February Assume that the profit function for
Crm Store
Save
40
20
10
1 2 3 4 5 6 7 8 9 10 11 12
Month
a) Write the profit function for The Christmas Store as a function of the month
and sketch its graph
b)
Write the profit function for The Pool Store as a function of the month and
sketch its graph.
are are length
Write the total profit as a function of the month and sketch its graph. What is
the period?
are inside the
est enth of a
Use the maximum feature of a graphing calculator to find the owner's maxi-
mum total profit and the month in which it occurs.
Find the owner's minimum total profit and the month in which it occurs.
We know that y -a sin x + bcos x is a sine function. However, the sum of
two arbitrary sine or cosine functions is not necessarily a sine function. Find an
example in which the graph of the sum of two sine functions does not look like
a sine curve.
Explain.
is tangent to one
Answer:
what
Step-by-step explanation:
The equations x + 5 y = 10, 3 x minus y = 1, x minus 5 y = 10, and 3 x + y = 1 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, negative 1) and (1, 2). Blue line goes through (0, 1) and (1, negative 2). Pink line goes through (0, 2), and (2, 1.5). Orange line goes through (negative 2, negative 2.5) and (2, negative 1.5). Which is the approximate solution for the system of equations x + 5 y = 10 and 3 x + y = 1? (–0.3, 2.1) (–0.3, –2.1) (0.9, –1.8) (0.9, 1.8)
Answer:
A: (–0.3, 2.1)
Answer:a
Step-by-step explanation:
Solve the simultaneous equations 2x-y=7 3x+y=3
Answer:
( 2 , - 3 )Step-by-step explanation:
Using elimination method:
2x - y = 7
3x + y = 3
--------------
5x = 10
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{10}{5} [/tex]
Calculate
[tex]x = 2[/tex]
Now, substitute the given value of X in the equation
3x + y = 3
[tex]3 \times 2 + y = 3[/tex]
Multiply the numbers
[tex]6 + y = 3[/tex]
Move constant to R.H.S and change it's sign
[tex]y = 3 - 6[/tex]
Calculate
[tex]y = - 3[/tex]
The possible solution of this system is the ordered pair ( x , y )
( x , y ) = ( 2 , -3 )---------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
[tex]2 \times 2 - ( - 3) = 7[/tex]
[tex]3 \times 2 - 3 = 3[/tex]
Simplify the equalities
[tex]7 = 7[/tex]
[tex]3 = 3[/tex]
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( 2 , - 3 )Hope this helps..
Best regards!!
What is the value of x in the equation 5 (4 x minus 10) + 10 x = 4 (2 x minus 3) + 2 (x minus 4)?
Answer:
x = 1.5
Step-by-step explanation:
5(4x-10)+10x=4(2x-3)+2(x-4)
Distribute(5)
20x-50+10x=4(2x-3)+2(x-4)
Distribute(4)
20x-50+10x=8x-12+2(x-4)
Distribute(2)
20x-50+10x=8x-12+2x-8
Combine like terms
30x-50=10x-20
Subtract(10x)
20x-50=-20
Add(50)
20x=30
Divide(20)
x = 1.5
Hope it helps <3
Answer:
x = 3/2Step-by-step explanation:
5 ( 4x - 10) + 10x = 4(2x - 3) + 2(x - 4)
Expand the terms
That's
20x - 50 + 10x = 8x - 12 + 2x - 8
Simplify
30x - 50 = 10x - 20
Group the constants at the right side of the equation
That's
30x - 10x = - 20 + 50
20x = 30
Divide both sides by 20
x = 3/2
Hope this helps you
How does the frequency of f(x) = cos(2x) relate to the frequency of the parent function cos x?
Answer:
The frequency of f(x) is two times the frequency of the parent function.
Step-by-step explanation:
We can say that the number that is beside the x is equal to [tex]2\pi *f[/tex], where f is the frequency.
Then, for the parent function, we get:
[tex]1 = 2\pi f_1[/tex]
or solving for [tex]f_1[/tex]:
[tex]f_1=\frac{1}{2\pi }[/tex]
At the same way, for f(x), we get:
[tex]2=2\pi f_2\\f_2=2(\frac{1}{2\pi })[/tex]
But [tex]\frac{1}{2\pi }[/tex] is equal to [tex]f_1[/tex], so we can write the last equation as:
[tex]f_2=2f_1[/tex]
It means that the frequency of f(x) is two times the frequency of the parent function.
Select the correct answer. Brad is planting flowers in a grid-like pattern in his garden. He is trying to determine the possible numbers of rows and columns in which he can plant his flowers. He determines that two possibilities are 8 rows and 25 columns or 10 rows and 20 columns. What is the constant of proportionality in this inverse variation?
Answer:
[tex]C.\ 200[/tex]
Step-by-step explanation:
Given
Let R represents rows and C represents Columns
When R = 8, C = 25
When R = 10, C = 20
Required
Given that there exist an inverse variation, determine the constant of proportionality;
We start by representing the variation;
[tex]R\ \alpha \ \frac{1}{C}[/tex]
Convert proportion to an equation
[tex]R\ = \ \frac{k}{C}[/tex]
Where k is the constant of proportion;
[tex]R * C\ = \ \frac{k}{C} * C[/tex]
Multiply both sides by C
[tex]R * C\ = k[/tex]
Reorder
[tex]k = R * C[/tex]
When R = 8, C = 25;
The equation [tex]k = R * C[/tex] becomes
[tex]k = 8 * 25[/tex]
[tex]k = 200[/tex]
When R = 10, C = 20;
The equation [tex]k = R * C[/tex] becomes
[tex]k = 10 * 20[/tex]
[tex]k = 200[/tex]
Hence, the concept of proportionality is 200
Which of these is the opposite reciprocal of 3/4
Answer: -4/3
Step-by-step explanation: To find the negative reciprocal of a fraction, all you have to do is flip the fraction and change the sign.
So the negative reciprocal of 3/4 is -4/3.
What is the distance to the earth’s horizon from point P? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer:
156.7 miles
Step-by-step explanation:
Since [tex]x[/tex] is tangent to the circle, then it is also a right angle with the radius, from here, just do Pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to solve for [tex]x[/tex].
Since 1 leg and the hypotenuse is given to you, you want to solve for the other leg, which is [tex]x[/tex] (either [tex]a[/tex] or [tex]b[/tex]). Lets use [tex]b[/tex] for [tex]x[/tex] and set up the equation.
[tex]b^{2}=c^2-a^2[/tex]
[tex]b^2=(3959+3.1)^2-3959^2[/tex]
[tex]b^2 = 3962.1^2 - 3959^2[/tex]
[tex]b^2 = 15,698,236.41 - 15,673,681[/tex]
[tex]b^2 = 24,555.41[/tex]
[tex]\sqrt{b^2}=\sqrt{24,555.41}[/tex]
[tex]b=156.7016592[/tex]
[tex]b=156.7[/tex] (round to nearest tenth)
The distance to the earth’s horizon from point P is 281.6 miles
What is distance?The distance between two points is the length of the line joining the two points. Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
here, we have,
to determine the distance to the earth’s horizon from point P:
The tangent line from P meets the radius of the earth at a right angle.
This means that the triangle is a right triangle.
The length of x is then calculated as:
(3959 + 10)^2= 3959^2 + x^2
Rewrite as:
x^2 = (3959 + 10)^2- 3959^2
Evaluate
x^2 = 79280
Take the square root of both sides
x = 281.6
Hence, the distance to the earth’s horizon from point P is 281.6 miles
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Helppppppp ASAP pleaseee
Answer:
True
Step-by-step explanation:
Inverse variation on a graph is depicted by the movement of the graph diagram (line) in a downward motion
Answer:true
Step-by-step explanation:
Taylor and Jeff have been selling frozen pizzas for a class fundraiser. Taylor has sold half as many
pizzas as Jeff. Together they have sold a total of 126 pizzas. How many pizzas did Taylor sell?
Answer:
Taylor sold 42 pizzas
Step-by-step explanation:
Make a system of equations where t represents the number of pizzas Taylor sold and j represents the number that Jeff sold:
t + j = 126
j = 2t
We can solve this system by substitution, since we can substitute 2t as j.
t + j = 126
t + 2t = 126
3t = 126
t = 42
Taylor sold 42 pizzas.
Answer:
Step-by-step explanation:
Let x represent the number of pizzas that Tailor sold.
Let y represent the number of pizzas that Jeff sold.
Together they have sold a total of 126 pizzas. This means that
x + y = 126- - - - - - - - -1
Taylor has sold half as many
pizzas as Jeff. This means that
x = 1/2 × y = y/2
Substituting x = y/2 into equation 1, it becomes
y/2 + y = 126
Multiplying both sides of the equation by 2, it becomes
y + 2y = 252
3y = 252
y = 252/3
y = 84
x = y/2 = 84/2
x = 42
Taylor sold 42 pizzas
Which two points are on the graph of y=-x+ 3?
(-1,-2), (1,4)
(1, 2), (0, -3)
(0, 3), (4, -1)
(4, -1), (1, 3)
Answer:
(0, 3), (4, -1)
(1, 2)
Step-by-step explanation:
If the answers that have been provided to you are only in pairs then it'd just be the first answer I wrote. The points (1, 2) also are on the graph of y=x+3 but if the answers aren't individual than I'd just stick with the (0, 3), (4, -1). Does that make sense? I used a graphing calculator online called Desmos, it's very good. I highly recommend it for problems like these.
I hope this helps:) Select as brainliest because I actually put work into this and tried.
Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is the smallest data value. C. The mean does not represent the center because it is the largest data value. D. The mean does not represent the center because it is not a data value. E. There is no mean age.
Answer:
A. The mean represents the center.
A. The median represents the center.
B. The mode does not represent the center because it is the smallest data value.
Step-by-step explanation:
Mean
(9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11)/13 = 120/13 = 9.2
The mean 9.2 and it represents the center of data.
Median
By arranging the set of data, the median, the median is the center number
8,8,8,8,8,8,(9),9,9,10,11,12,12
The median is 9 and it represents the center of data.
Mode
The mode is the number that appears most in the set of data.
The number that appears most in the set of data is 8 and does not represent the set of data.
Given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:
the mean is: 9.2the median is: 9the mode is: 8A. The mean does represents the center of the data set
Given the following data set:
9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8, 11
Let's find the mean, median, and mode.
Mean of the data set:
Mean = sum of all values / number of values
Mean = [tex]\frac{9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11}{13}[/tex]
Mean = [tex]\frac{120}{13} = 9.2[/tex]
Median of the data set:
Order the data from the least to the greatest then find the middle value.
Thus:8, 8, 8, 8, 8, 8, (9,) 9, 9, 10, 11, 12, 12
The middle value is 9.
The median = 9Mode of the data set:
The mode = the data value that appears most
8 appeared the most, therefore, the mode = 8
If you observe, you will note that the mean and median of the data set are similar. We can as well conclude that the mean represents the center of the data set.
In summary, given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:
the mean is: 9.2the median is: 9the mode is: 8A. The mean does represents the center of the data set
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At the start of 2010 karim had rm5000
Step-by-step explanation:
Tell the whole question please
Please answer this correctly without making mistakes
Answer:
d = 115.4 mi
Step-by-step explanation:
Since it gives us the distance in between the locations, we simply label the distances:
From the Garbage to the Hotel is 58.3 miles.
From the Hotel to the Hardware Store is 57.1 miles.
We are trying to find the distance from the Garbage to the Hardware Store, we simply add the distances between:
58.3 mi + 57.1 mi = 115.4 mi
What is 25÷5what is 25 / 5
Answer:
5
Step-by-step explanation:
25/5
=5✖️5=25
=5/1
Answer:
25÷5 = 5 and 25/5 = 125
Step-by-step explanation:
hope this helps!
URGENT
What is the length of?
Answer:
option (c) 4
Step-by-step explanation:
sides opposite to equal angles are equal
so ML = MN
that is 4x = x+3
4x - x = 3
3x = 3
x= 1
ML= 4x = 4*1 = 4 units
MN = x+3= 1+3= 4 units
so answer is option (c) 4
hope this answer help you
magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. What values do , , n, E, and p represent? If the confidence level is %, what is the value of ?
Complete Question
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12 % chose chocolate pie, and the margin of error was given as plus or minus 5 percentage points.What values do [tex]\r p , \ \r q[/tex], n, E, and p represent? If the confidence level is 90%, what is the value of [tex]\alpha[/tex] ?
Answer:
a
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e [tex]\r q = 1- \r p[/tex]
b
[tex]\alpha = 10\%[/tex]
Step-by-step explanation:
Here
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e
[tex]\r q = 1- \r p[/tex]
[tex]\r q = 1- 0.12[/tex]
[tex]\r q = 0.88[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as
[tex]\alpha = ( 100 - C )\%[/tex]
Where [tex]C[/tex] is the confidence level which is given in this question as [tex]C = 90 \%[/tex]
So
[tex]\alpha = ( 100 - 90 )\%[/tex]
[tex]\alpha = 10\%[/tex]
It took Malik 1 hour and 30 minutes to complete his English essay. He finished the essay at 5:30 pm. What time did he start working on the essay?
Answer:
4:00 pm
Step-by-step explanation:
To find the time it takes Malik to finish his English essay, let's start by subtracting one hour.
5:30 minus 1 hour is 4:30.
Now, subtract 30 minutes.
4:30 minus 30 minutes is 4:00.
Malik started working on his English essay at 4:00 pm.
Hope that helps.