Answer:
an = 115 + (n - 1) (-6)
a25 = - 29
Step-by-step explanation:
We use the definition for the nth term of an arithmetic sequence:
an = a1 + (n - 1) d
a5 = 91 = a1 + (5 - 1) d
91 = a1 + 4 d
a20 = 1 = a1 + (20 - 1) d = a1 + 19 d
1 = a1 + 19 d
now we subtract term by term one expression from the other
90 = 4 d - 19 d
90 = - 15 d
divide both sides by -15 to isolate d
d = 90 / (-15) = -6
Now we can calculate what a1 is using for example:
1 = a1 + 19 d
1 = a1 - 114
add 114 to both sides:
115 = a1
Then our general expression for the sequence is:
an = 115 + (n - 1) (-6)
We can now use it to calculate the value of a25:
a25 = 115 + (24) * (-6) = -29
Write the sentence as an equation.
w added to 293 is 326
Answer:
let no be x
293+x=326
x=326-293=33
33 is needed to add.
Solve the equation. -5(-4+2n)=-10(n-2)
Answer:
0 = 0 means that there are infinite solutions.
Step-by-step explanation:
Equation is -5(-4+2n)=-10(n-2)
1. Distribute the -5 and -10
20 -10n = -10n + 20
2. Subtract 20 from one side to the other to get only 1 variable on 1 side.
-10n = -10n
3. divide -10 to separate the variable from the constant.
n = n
This means there are infinite solutions.
12.
The ratio of boys to girls in a class is 3:7. Write down the fraction of the class who are boys.
Answer:
let tle number of boys and girls be 2x and3x
Step-by-step explanation:
like this solve the question
The difference of two supplementary angles is 70 degrees. Find the measures of the angles.
Answer:
DUEDY A. 32 degrees
Step-by-step explanation:
PATROLLING WEE WOOO
Xd
Answer:
55 125
Step-by-step explanation:
Let the smaller angle = x
Let the larger angle = x + 70
They are supplementary so the total of the two angles, by definition must be 180 degrees. Note that you should understand that any number of angles can but supplementary as long as they all add up to 180 degrees.
x + x + 70 = 180
2x + 70 = 180
2x + 70 - 70 = 180 - 70
2x = 110
2x/2 = 110/2
x = 55
the smaller angle = 55 degrees
The larger angle = 55 + 70 = 125
(1) y - 11 = 4
(2) y = 2x + 3
Answer:
y = 15 , x = 6
Step-by-step explanation:
you can easily find y from first equation
Move y to the other side of the equation and reverse its sign
so (-11) changes to (+11) and now we have this equation
y = 15
now you must replace 15 instead of y in second equation ,then we have this equation
15 = 2x + 3
now we have to find x
move (+3) to other side of equation and reverse its sign
(+3) changes to (-3)
we have this equation now
15 - 3 = 2x
12 = 2x
x = 12 ÷ 2 = 6
if my annual income $168,000 what would my monthly gross be
To get the monthly gross, divide the annual income into 12:
Then, the monthly gross is $14,000
A fair spinner has 9 equal sections: 2 red, 3 blue and 4 green.
It is spun twice
What is the probability of not getting two consecutive reds?
OP
Answer:
The Probability of not getting two consecutive reds is 0.9506
Step-by-step explanation:
Number of sections = 9
Number of red sections = 2
Number of blue sections = 3
Number of green sections = 4
Probability of getting two consecutive reds = \(\frac{2}{9} \times \frac{2}{9}=\frac{4}{81}\)
So,The Probability of not getting two consecutive reds =\(1- \frac{4}{81}=\frac{77}{81}=0.9506\)
Hence The Probability of not getting two consecutive reds is 0.9506
Plssss help I’ll mark u brainliest!!!
Answer:
The answer to the question is C
Use the appropriate form of the percentage formula.What percent of 15.1 is 13.6? Round to the nearest hundredth of a percent."
In order to find the corresponding percent, we divide the amount we are looking for by the total and multiply by 100 to make it a percentage, then
\(\begin{gathered} \frac{13.6}{15.1}=0.90066 \\ mu\text{ltiply by 100} \\ 0.90066=90.07\text{\%} \end{gathered}\)someone please help me with this question thank you :)
Answer:
The other leg = 8 cm
Step-by-step explanation:
a^2 + b^2 = c^2
a^2 + (15)^2 = (17)^2
a^2 + 225 = 289
a^2 = 64
a = 8
Answer:
its 225
Step-by-step explanation:
9. Zola solved a question on her math test that. asked her to find the volume of the sphere shown
below in terms of T. Explain Zola's error and solve for the correct answer.
d=11 in
v-(-X5.5¹)
V=((16.5)
V = 22π in³
if d=11 in then the volume of the sphere=697.19
\(V=\frac{4}{3} \pi d\)
\(V=\frac{4}{3} *\frac{22}{7} *5.5^{3} =697.19\)
The amount of room a spherical occupies inside is its volume. Because every point on the sphere's surface is equally spaced from its center, the sphere can be considered a three-dimensional round solid object. The fixed point and fixed distance, respectively, represent the sphere's center and radius. V = 4/3 r3, where r is the radius and V is the volume, is the formula for a sphere's volume. The radius of a sphere is equal to half its diameter. A circle and a sphere are both round, if you compare them. As the sphere is a three-dimensional object rather than a two-dimensional circle, we can estimate its volume and surface area.
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State all integer values of xx in the interval \left[-1, 5\right][−1,5]
Answe67
Step-by-step explanation:
There are 3 cats in a room and no other creatures.each cat has 2 ears, 4 paws, and 1 tail
Answer: theres really no question here
Step-by-step explanation:
1) Find the interior angle sum of a 36-gon.
6120°
720°
900°
1800º
Sum of interior angles = ( number of sides -2) x 180 degrees.
Sum = (36-2) x 180
Sum = 34 x 180
Sum = 6,120 degrees.
The length of a movie falls on a normal distribution. About 95% of movies fall between 75 minutes and 163 minutes.
Required:
a. What is the mean value for average movie length in minutes?
b. What is the value of the standard deviation for average movie length in minutes?
Answer:
a) x = 119 minutes
the mean value for average movie length in minutes is 119 minutes
b) margin of error M.E = 44 minutes
Note; Since the number of samples used is not given, the standard deviation r cannot be calculated using the equation
M.E = zr/√n
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-M.E
M.E = zr/√n
Given that;
M.E = margin of error
Mean = x
Standard deviation = r
Number of samples = n
Confidence interval = 95%
z value (at 95% confidence) = 1.96
a) The mean value x can be calculated as;
x = (a+b)/2
Where a and b are the lower and upper bounds of the confidence interval;
a = 75 minutes
b = 163 minutes
substituting the values;
x = (75+163)/2
x = 119 minutes
the mean value for average movie length in minutes is 119 minutes
b) the margin of error M.E can be calculated as;
M.E = (b-a)/2
Substituting the values;
M.E = (163-75)/2
M.E = 44 minutes
Since the number of samples used is not given, the standard deviation r cannot be calculated using the equation
M.E = zr/√n
$16.20 per hour for 40 hours and time and a half for 8 hours. What is the total pay?
Answer:
Add 16.20+ 40+8
Step-by-step explanation: 16+20+40+8= 84
At the park there is a pool shaped like a circle with diameter 22 yd. A ring-shaped path goes around the pool. Its
width is 5 yd. If one gallon of coating can cover 5yd many gallons of coating do we need? Note that coating comes only by the gallon so the number of gallons must be a whole number. (Use the value 3.14 for pi.)
Answer: To find the area of the ring-shaped path, we need to subtract the area of the inner circle (the pool) from the area of the outer circle. The radius of the pool is half the diameter, so it is 11 yards. The radius of the outer circle is the sum of the radius of the pool and the width of the path, so it is 11 + 5 = 16 yards.
The area of the pool is:
A_pool = pi * r^2 = pi * 11^2 ≈ 380.13 square yards
The area of the outer circle is:
A_outer = pi * R^2 = pi * 16^2 ≈ 804.25 square yards
The area of the ring-shaped path is:
A_path = A_outer - A_pool ≈ 804.25 - 380.13 ≈ 424.12 square yards
Since one gallon of coating can cover 5 square yards, we need:
Gallons = A_path / 5 ≈ 424.12 / 5 ≈ 84.82
Therefore, we need approximately 85 gallons of coating to cover the ring-shaped path.
Step-by-step explanation:
Use π = \frac{22}{7}: Henry bought exactly the right amount of fencing to put around his circular herb garden, which has a diameter of 14 feet. Then he decides to make the garden larger by doubling the diameter. How much more fencing does Henry need to purchase to enclose the new garden?
The answer of the given question based on the circle is , Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.
What is Circumference?Circumference is distance around edge of circular object. It is same as perimeter of circle. The circumference of a circle can be calculated using the radius of the circle, which is half the diameter.
The circumference of circle with diameter d is given :
C = πd
Using the given diameter of 14 feet, the circumference of the original garden is:
C1 = πd1 = (22/7) * 14 = 44 feet
When the diameter is doubled to 28 feet, the circumference of the new garden is:
C2 = πd2 = (22/7) * 28 = 88 feet
To find how much more fencing Henry needs to purchase to enclose the new garden, we need to subtract the original circumference from the new circumference:
C2 - C1 = 88 - 44 = 44 feet
Therefore, Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.
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need help asap please
Answer:
\(\displaystyle 40\)
Step-by-step explanation:
This is an isosceles triangle, therefore you must double up DA to get 40.
I am joyous to assist you at any time.
PLEASE HELP FAST!! IT IS URGENT!!
Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B = the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What iS the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here.
O 0.159
O 0.259
O 0.448
O 0.741
Step-by-step explanation:
The probability that Becky's proportion of poses held for over a minute is greater than Carla's is 0.741.
This can be determined by using the z-table, which shows the probability that a random variable is in the range that is a certain distance away from the mean.
In this case, we are looking at the probability that a random variable is greater than C, so we use the z-value for 0.741.
Which data set contains an outlier?
A. {15, 15, 15, 16, 16, 17, 18}
B. {45, 46, 47, 47, 49, 49}
C. {9, 10, 10, 11.4, 12.1, 12.6}
D. {16, 42, 45, 45, 46, 48}
The data set which contains an outlier from the given answer choices is; Choice D; {16, 42, 45, 45, 46, 48}.
What is an outlier?An outlier in a set of data values is a data value which differs significantly from other data points and hence, tends to affect the mean of such set of data values significantly.
On this note, choice D is the set of data values which contains an outlier.
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Find the value of n for which the division of x^2n-1 by x+3 leave remainder of -80.
The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.
To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:
Write the dividend and divisor in polynomial long division format:
_________________________
x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...
Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).
Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).
Subtract the result obtained in step 3 from the original dividend:
x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...
Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.
Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.
-3x^(2n-2) + 0x^(2n-3) + ... = -80
Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.
This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:
2n-2 = 0
2n = 2
n = 1
Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.
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HELP PLEASE! E lies in the interior of
m
m
m
Show Your Work
Rupert is a teacher and has his blood pressure taken
Mark on the above diagram a reading of:
Systolic = 130, Diastolic = 95
What does this tell us about Rupert's blood pressure?
Based on the readings of 130/95, we can conclude that Rupert's blood pressure is within a generally healthy range, but the diastolic reading is slightly elevated.
Based on the given readings of 130 for the systolic blood pressure and 95 for the diastolic blood pressure, we can analyze Rupert's blood pressure using the provided blood pressure chart.
According to the chart, the systolic blood pressure reading of 130 falls within the range of "Ideal blood pressure." This indicates that Rupert's systolic blood pressure is within a healthy range.
The diastolic blood pressure reading of 95 falls slightly above the upper limit of the "Ideal blood pressure" range but is below the threshold of 100, which marks the beginning of the "Pre-high blood pressure" range. Although it is slightly elevated, it is not classified as high blood pressure.
It is important to note that blood pressure can vary throughout the day and in different situations, so a single reading may not provide a comprehensive assessment of one's overall blood pressure health. It is recommended to monitor blood pressure over time and consult a healthcare professional for further evaluation and advice.
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Verify that the given point is on the curve and find the lines that are a. tangent and b. normal to the curve at the given point.
Answer:
4, -4, 16, 16, truetangent: x - y = 8normal: y = -xStep-by-step explanation:
You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.
PointThe point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.
(a) TangentThe tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...
m = y/x = -4/4 = -1
The tangent line's slope is the opposite reciprocal of this:
m = -1/(-1) = 1
The point-slope form of the equation for the tangent line is ...
y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)
y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)
x -y = 8 . . . . . . . . . . add 4-y to put in standard form
The equation of the tangent line is x - y = 8.
(b) NormalIn the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...
y -0 = -1(x -0)
y = -x
The equation of the normal line is y = -x.
__
Additional comment
The normal line can also be written as x + y = 0.
The tangent line can also be written as y = x -8.
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If $8000 is invested at 5% compounded quarterly , what is the amount after 6 years?
Rather than being irrelevant or unhelpful, residuals in a simple linear regression model can be quite informative. Which of the following, in your opinion, residuals might indicate about the underlying population and the model?
Regression analysis will indicate about the underlying population and the model.
It is one of the most used and most powerful multivariate statistical techniques for it infers the existence and form of a functional relationship in a population. Once you learn how to use regression, you will be able to estimate the parameters { the slope and intercept } of the function that links two or more variables. With that estimated function, we will be able to infer or forecast things like unit costs, interest rates, or sales over a wide range of conditions.
Though the simplest regression techniques seem limited in their applications, statisticians have developed a number of variations on regression that greatly expand the usefulness of the technique. And again, the t-distribution and F-distribution will be used to test hypotheses.
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Let XY be a random draw from the following box of tickets0 0 1 1 21 2 0 1 0Find E(X+Y)^2
We can start by finding the expected value of X and Y separately: (X) = (0+0+1+1+2+1+0+1+0)/9 = 6/9 = 2/3, E(Y) = (0+0+1+1+2+0+1+0+0)/9 = 5/9
Next, we can expand (X+Y)^2: (X+Y)^2 = X^2 + 2XY + Y^2
Taking the expected value of both sides, we get: E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2)
To find E(XY), we can create a table of the possible values of X and Y, and their corresponding probabilities: [table in the attatchment]
So, we have:
E(XY) = 0*(3/9) + 0*(2/9) + 0*(1/9) + 0*(2/9) + 1*(1/9) + 2*(1/9) + 0*(1/9) + 2*(1/9) + 4*(1/9) = 1
Next, we need to find E(X^2) and E(Y^2): E(X^2) = (0^2+0^2+1^2+1^2+2^2+1^2+0^2+1^2+0^2)/9 = 8/9
E(Y^2) = (0^2+0^2+1^2+1^2+2^2+0^2+1^2+0^2+0^2)/9 = 5/9
Putting it all together, we get: E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2) = 8/9 + 2*1 + 5/9 = 23/9. Therefore, the answer is 23/9.
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A particle P moves on the positive x-axis. The velocity of P at time t seconds is
(2t2 – 9t + 4) ms-1. When t= 0, P is 15 m from the origin O.
It can be shown that P is instantaneously at rest whent = 1 and when t = 4.
==
Find the total distance travelled by P in the interval 0
(5 marks)
Using integration, it is found that the total distance traveled by P in the interval between 0 and 4 seconds was of 230.67 meters.
What is the role of derivatives in the relation between acceleration, velocity and position?The velocity is the derivative of the position, hence the position is the integrative of the velocity.The acceleration is the derivative of the velocity, hence the velocity is the integrative of the acceleration.In this problem, the velocity is:
\(v(t) = 2t^2 - 9t + 4\)
Then, the position will be given by:
\(s(t) = \int v(t) dt\)
\(s(t) = \int (2t^2 - 9t + 4) dt\)
\(s(t) = \frac{2t^3}{3} - \frac{9t^2}{2} + 4t + K\)
Considering that when t = 0, P is 15 m from the origin O, K = 15, and:
\(s(t) = \frac{2t^3}{3} - \frac{9t^2}{2} + 4t + 15\)
The total distance traveled by P between 0 and 4 seconds is:
\(D = \int_{0}^{4} s(t) dt\)
\(D = \int_{0}^{4} \left(\frac{2t^3}{3} - \frac{9t^2}{2} + 4t + 15\right) dt\)
\(D = \left(\frac{t^4}{6} - \frac{3t^3}{2} + 2t^2 + 15t + K\right)_{t = 0}^{t = 4}\)
Then, applying the Fundamental Theorem of Calculus:
\(D(4) = \frac{4^4}{6} - \frac{3(4)^3}{2} + 2(4)^2 + 15(4) = 230.67\)
\(D(0) = \frac{0^4}{6} - \frac{3(0)^3}{2} + 2(0)^2 + 15(0) = 0\)
\(D = D(4) - D(0) = 230.67 - 0 = 230.67\)
The total distance traveled by P in the interval between 0 and 4 seconds was of 230.67 meters.
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cacula las dimensiones de un rectangulo sabiendo que su area es de 66cm y su base mide 5cm mas que su altura
Answer:
Calcular las dimensiones de un rectángulo, sabiendo que es 4cm más largo que ancho y ... Área = base•altura ... Encuentra más respuestas.
Step-by-step explanation:
Answer:
how do you translate?
Step-by-step explanation: