The volume of the solid is 284π/3 cubic inches.
To find the volume of the solid, we need to break it down into simpler shapes and then calculate their volumes separately.
The solid is made up of a cylinder and a hemispherical hole cut from the top of it. Let's first calculate the volume of the cylinder. The height of the cylinder is given as 12 inches and the radius can be calculated as half of the hypotenuse of the triangle (which is 10 inches). Therefore, the radius of the cylinder is 5 inches.
The formula for the volume of a cylinder is Vcylinder = πr^2h, where r is the radius and h is the height. Substituting the values, we get:
Vcylinder = π(5^2)(12) = 300π cubic inches
Now, let's calculate the volume of the hemispherical hole. The rim of the hole is 3 inches thick, which means the radius of the hole is (5 - 3) = 2 inches. The volume of a hemisphere is given by the formula Vhemisphere = (2/3)πr^3.
Substituting the values, we get:
Vhemisphere = (2/3)π(2^3) = 16π/3 cubic inches
Now, the volume of the solid can be found by subtracting the volume of the hemispherical hole from the volume of the cylinder:
Vsolid = Vcylinder - Vhemisphere
Vsolid = 300π - 16π/3
Vsolid = 284π/3 cubic inches
Therefore, the volume of the solid is 284π/3 cubic inches.
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8x^2+18x+9
Box method
Answer:
144x^3+9
Step-by-step explanation:
First of all multiply 8x^2 and 18x then it is 144
Write the polynomial as the product of linear factors. g(x) = x3 – 3x2 + x + 5 g(x) =________ List all the zeros of the function. (Enter your answers as a comma-separated list.) X =__________
The polynomial g(x) can be written as the product of linear factors g(x) = (x - 5)(x - 1)(x + 3). Polynomial as the product of linear factors. g(x) = x3 – 3x2 + x + 5 g(x) = (x - 5)(x - 1)(x + 3) and all the zeroes of the function are x = 5, 1, and -3.
To find the zeros of a function, we need to set each factor of the polynomial to zero and solve for x. When x = 5, (x - 5) = 0, when x = 1, (x - 1) = 0, and when x = -3, (x + 3) = 0.
Therefore, the zeros of the function are x = 5, 1, and -3. We can use these zeros to graph the function, as each zero is a point on the x-axis. The graph of this function will have three x-intercepts at the given points. We can also use the zeros to find the y-intercept, which will be the constant term in the polynomial.
In this case, the constant term is 5, so the y-intercept will be (0, 5) the polynomial g(x) = (x - 5)(x - 1)(x + 3) has zeros at x = 5, 1, and -3, and a y-intercept at (0, 5).
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A store is planning on having New Year's sale in which all winter coats will be discounted by 60%. Find the sale price of a coat that
has a regular price of $80
Answer:
$32
Step-by-step explanation:
Since the coats are discounted by 60%, we need to find 100-60=40% of the original price.
We need to find 40% of 80.
We can use proportional relationships.
100%=80
10%=8
40%=32
Christian's money from his job increased from $12 hour to $21 hour. What is the percent increase?
Answer:
75%
Step-by-step explanation:
Starting value: 12
Final Value: 21
Subtract final value minus starting value
Divide that amount by the absolute value of the starting value
Multiply by 100 to get percent increase
If the percentage is negative, it means there was a decrease and not an increase.
The air temperature decreases about 5°F for each increase of 1,000 feet in altitude. If the outside temperature at ground level in a certain location is 68°F, then the air temperature y is represented by the function y=−5x+68 , where x is the altitude (in thousands of feet).
Which of the following sets of numbers would be appropriate input values for the given situation? Select all that apply.
Multiple select question.
cross out
A)
By answering the above question, we may infer that The input value 0 equation represents the height at sea level, making it an inappropriate value for this function.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
For the predicament, the following input values would be suitable:
B) 1
C) 2
D) 3
E) 4
As the temperature drops by around 5°F for every 1,000 feet of height, we must utilise altitude numbers in thousands of feet to obtain the function's proper input values. Hence, we would utilise a value of 1 as an input for every 1,000 feet of height rise. Consequently, 1, 2, 3, and 4 would be the proper input values, which correspond to altitudes of 1,000, 2,000, 3,000, and 4,000 feet, respectively. The input value 0 represents the height at sea level, making it an inappropriate value for this function.
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Determine the Equation of circle A
Answer:
Step-by-step explanation:
When writing the equation for a circle on a plane, we use the format:
[tex](x-x_{1})^2+(y-y_{1})^2=r^2[/tex]
x1 and y1 is the point of the center of the circle, which in this case is (1,-2)
r represents the radius, which is the distance from the center to the edge of the circle, which is (4,-2) - (1,-2) = 3
Our equation is now:
[tex](x-1)^2+(y+2)^2=9[/tex]
the reason why its y+2 is because (y-(-2) = (y+2)
r is squared, which is why it's 9 instead of 3. Hope this helps!
1. FIND THE EXPECTED VALUE OF A GAME IN WHICH YOU HAVE A (1/20) CHANCE OF WINNING AND A (19/20) CHANCE OF LOSING. IF YOU WIN YOU RECEIVE $300 PLUS THE $15 IT COST TO PLAY THE GAME. IF YOU LOSE YOU LOSE THE $15.00
2. IF TEST SCORES ARE NORMALLY DISTRIBUTED WITH A MEAN OF 84 AND A STANDARD DEVIATION OF 9. PLEASE FIND THE PROBABILITY A STUDENT SCORED BETWEEN 75 AND 89.
3. FIND THE PROBABILITY A STUDENT SCORED ABOVE 85.
The expected value of the game in which you have a (1/20) chance of winning is $1.50. The probability of a student scoring between 75 and 89 is 0.5536. The probability of a student scoring above 85 is 0.4562.
1. To find the expected value of the game, we need to multiply the probability of each outcome by the value of that outcome and then add them together.
E(X) = (1/20)($300 + $15) + (19/20)(-$15)
E(X) = $315/20 - $285/20
E(X) = $30/20
E(X) = $1.50
So the expected value of the game is $1.50.
2. To find the probability of a student scoring between 75 and 89, we need to use the z-score formula:
z = (x - μ)/σ
For x = 75, z = (75 - 84)/9 = -1
For x = 89, z = (89 - 84)/9 = 0.56
Using a z-table, we can find the probability of a student scoring between these two z-scores:
P(-1 < z < 0.56) = P(z < 0.56) - P(z < -1)
P(-1 < z < 0.56) = 0.7123 - 0.1587
P(-1 < z < 0.56) = 0.5536
So the probability of a student scoring between 75 and 89 is 0.5536.
3. To find the probability of a student scoring above 85, we need to use the z-score formula:
z = (x - μ)/σ
For x = 85, z = (85 - 84)/9 = 0.11
Using a z-table, we can find the probability of a student scoring above this z-score:
P(z > 0.11) = 1 - P(z < 0.11)
P(z > 0.11) = 1 - 0.5438
P(z > 0.11) = 0.4562
So the probability of a student scoring above 85 is 0.4562.
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The area of a circle is 1.1304 square kilometers. What is the circle's diameter? Use 3.14 for .
Answer:
Step-by-step explanation:
the diameter of the circle is approximately 1.2 kilometers.
We can use the formula for the area of a circle:
Area = pi x (diameter/2)^2
where pi is a constant approximately equal to 3.14, and diameter is the distance across the circle passing through its center.
We are given the area of the circle as 1.1304 square kilometers, so we can substitute this value into the formula and solve for diameter:
1.1304 = 3.14 x (d/2)^2
1.1304 = 0.785d^2
d^2 = 1.1304/0.785
d^2 = 1.440
d = sqrt(1.440)
d ≈ 1.2
Therefore, the diameter of the circle is approximately 1.2 kilometers.
Find angle A on a triangle when A(5x-1) B is unknown and C(2x)?
Answer:
∠A = 64°
Step-by-step explanation:
You have a triangle inscribed in a semicircle with acute angles marked A=(5x-1)° and C=(2x)°.
Right triangleA triangle inscribed in a semicircle is a right triangle. (You know that because angle B is half the measure of 180° arc AC.) That means the two marked angles total 90°:
(5x -1) +(2x) = 90
7x = 91
x = 13
Then angle A is ...
A = (5·13 -1)° = (65 -1)° = 64°
The measure of angle A is 64°.
__
Check:
C = (2x)° = (2·13)° = 26°
Then A+C = 64° +26° = 90°, as required.
a) The management of the Society would like to explore whether there is a difference in stress level between full-time and part-time volunteers. Conduct an appropriate hypothesis test, at 0.05 significance level, to ascertain this. State clearly your test statistic, degree of freedom and p-value. You may refer to the following SPSS report: Group Statistics Std. Error Mean Employment Status Stress Score (out of 50) Full-Time Part-Time N 336 195 Mean 41.4583 41.0564 Std. Deviation 5.28061 5.49901 .28808 39379 Independent Samples Test Levene's Test for Equality of Variances F Sig 1 df t-test for Equality of Means Mean Sig, (2-tailed) Difference 405 .40192 Std. Error Difference .48269 ess Score (out of 50) .066 .798 .833 529 Equal variances assumed Equal variances not assumed .824 392.166 .411 .40192 48792 (15 marks) b) For the above hypothesis test, compute and comment on the effect size. (5 marks)
a) The appropriate hypothesis test for this situation is an independent samples t-test. The test statistic is the t-value, which is 0.824 b) the above hypothesis test, compute and comment on The effect size is 0.074,
The null hypothesis is that there is no difference in stress level between full-time and part-time volunteers, and the alternative hypothesis is that there is a difference in stress level between full-time and part-time volunteers.
The test statistic is the t-value, which is 0.824. The degrees of freedom is 529, which is calculated by adding the sample sizes of the two groups (336 + 195) and subtracting 2. The p-value is 0.411, which is greater than the significance level of 0.05.
This means that we fail to reject the null hypothesis and conclude that there is no significant difference in stress level between full-time and part-time volunteers.
b) The effect size for this hypothesis test can be calculated using Cohen's d, which is the difference between the two group means divided by the pooled standard deviation.
The effect size is 0.074, which is considered a small effect. This means that the difference in stress level between full-time and part-time volunteers is small and may not be practically significant.
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Mabel ate dinner at a restaurant.The bill came to $79.If she left a 20% tip,how much was the tip?
The declaration made indicates that Mabel left a $15.80 gratuity.
How do the percentages translate?Percent, which is a relative number used to denote hundredths of any amount. Since one percent is equal to one tenth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.
To find the amount of the tip that Mabel left, we can multiply the bill amount by the tip percentage, which is 20% or 0.2 in decimal form.
The amount of the tip is:
Tip = Bill Amount x Tip Percentage
Tip = $79 x 0.2
Tip = $15.80
Therefore, the tip that Mabel left was $15.80.
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Find the midpoint \( M \) of the line segment joining the points \( A=(4,4) \) and \( B=(-6,-4) \).
The midpoint [tex]\( M \)[/tex] of the line segment joining the points [tex]\( A=(4,4) \)[/tex] and [tex]\( B=(-6,-4) \)[/tex] is [tex]\( M=(-1,0) \)[/tex].
To find the midpoint of a line segment, we can use the midpoint formula: [tex]\[ M=\left( \frac{x_1+x_2}{2})[/tex], [tex]\frac{y_1+y_2}{2} \right) \][/tex] where [tex]\( x_1 \)[/tex] and [tex]\( y_1 \)[/tex] are the coordinates of point [tex]\( A \)[/tex], and [tex]\( x_2 \)[/tex] and [tex]\( y_2 \)[/tex] are the coordinates of point[tex]\( B \)[/tex].
Plugging in the values from the given points, we get: [tex]\[ M=\left( \frac{4+(-6)}{2},\frac{4+(-4)}{2} \right) \][/tex]
Simplifying the fractions gives us: \[ M=\left( \frac{-2}{2},\frac{0}{2} \right) \]
Finally, we can simplify further to get our final answer:[tex]\[ M=(-1,0) \][/tex]
Therefore, the midpoint [tex]\( M \)[/tex] of the line segment joining the points [tex]\( A=(4,4) \)[/tex] and [tex]\( B=(-6,-4) \)[/tex] is [tex]\( M=(-1,0) \).[/tex]
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Which of the following scenarios does not represent an impulse purchase?
Melissa goes to get a $60 oil change and soon after decides to have her car windows tinted for $300 using her credit card.
Melissa goes to get a $60 oil change for her car but chooses to spend her money on $500 new car stereo speakers instead.
Melissa goes to get an oil change for her car but decides to save the $60 and ask her brother do the oil change for free.
The scenario that does not represent an impulse purchase is: Melissa goes to get an oil change for her car but decides to save the $60 and ask her brother to do the oil change for free.
An impulse purchase is an unplanned purchase made on the spur of the moment, without much consideration or planning. In the first scenario, Melissa goes to get an oil change but then decides to have her car windows tinted for $300, which is an additional expense that she had not planned for. This is an impulse purchase.
In the second scenario, Melissa goes to get an oil change but then decides to spend $500 on new car stereo speakers, which is again an additional expense that she had not planned for. This is also an impulse purchase.
However, in the third scenario, Melissa decides to save the $60 and ask her brother to do the oil change for free. This decision does not involve any additional expense or impulse purchase. Instead, it is a planned decision to save money by getting the oil change done for free. Therefore, this scenario does not represent an impulse purchase.
Answer:
Below
Step-by-step explanation:
The last choice is not an impulse purchase.....it is not a purchase at all.
the first two ARE impulse purchases.... she purchases something for which she initially had no intention.
Let f(x)=x2+6x+11.
What is the minimum value of the function?
Enter your answer in the box.
Step-by-step explanation:
The given function is a quadratic function with a positive leading coefficient, therefore it opens upwards and has a minimum value. To find the minimum value of the function, we can use the formula:
x = -b/2a
where a = 1 and b = 6 are the coefficients of the quadratic function.
x = -6/2(1) = -3
Substitute x = -3 into the function to find the minimum value:
f(-3) = (-3)^2 + 6(-3) + 11 = 2
Therefore, the minimum value of the function is 2.
2(3) to the power of 3 plus 5
Please help asap i need this badly
Answer:
75 seconds
Step-by-step explanation:
You want to know how long it took Sean to drink his slushy, given a graph of amount remaining versus time.
RemainingSean will have finished his slushy when the amount remaining is zero. That point on the graph occurs when the time is 75 seconds.
It takes 75 seconds for Sean to finish the slushy.
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PLEASE PLEASE HELP ME!!
(fog)(-9) value is -9 when f(x)=2x²-4x-15 and g(x)=x+12
What is a function?A relation is a function if it has only One y-value for each x-value.
The given functions are f(x)=2x²-4x-15 and g(x)=x+12
We need to find fog(-9)
Before that let us find fog(x)
f(g(x))=2(x+12)²-4(x+12)-15
f(g(-9))=2(-9+12)²-4(-9+12)-15
=2(3)²-4(3)-15
=18-12-15
=-9
Hence, (fog)(-9) value is -9 when f(x)=2x²-4x-15 and g(x)=x+12
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Decide whether it is possible for a triangle to have the three angle measures or three side lengths given.
If it is possible, then decide whether all such triangles are congruent.
(a) 30°, 80°, 70°
Triangle possible
Triangles with these measurements
▼(Choose one)
No triangle possible
(b) 20°, 105°, 55°
Triangle possible
Triangles with these measurements
▼(Choose one)
No triangle possible
(c) 4cm, 3cm, 8cm
Triangle possible
Triangles with these measurements
▼(Choose one)
No triangle possible
(d) 8cm, 15cm, 17cm
Triangle possible
Triangles with these measurements
▼(Choose one)
No triangle possible
(a) It is possible to form a triangle with the angle measures, 30°, 80°, 70°
It is not possible for all such triangles to be congruent.
(b) It is possible to form a triangle with the angle measures, 20°, 105°, 55°
It is not possible for all such triangles to be congruent.
(c) It is not possible to form a triangle with the side lengths, 4cm, 3cm, 8cm
(d) It is possible to form a triangle with these side lengths.
All such triangles are congruent
Determining if it is possible for a triangle to have the given angle measures or side lengths
From the question, we are to determine if it is possible for a triangle to have the given angle measures or side lengths
(a) To determine if a triangle can have the angle measures 30°, 80°, and 70°, we add the angles together to see if they equal 180°, the total degrees of a triangle.
30° + 80° + 70° = 180°
Since the angle measures add up to 180°, it is possible to form a triangle with these angle measures.
It is not possible for all such triangles to be congruent, since triangles with the same angle measures can have different side lengths.
(b) To determine if a triangle can have the angle measures 20°, 105°, and 55°, we add the angles together to see if they equal 180°.
20° + 105° + 55° = 180°
Since the angle measures add up to 180°, it is possible to form a triangle with these angle measures. However, it is not possible for all such triangles to be congruent, since triangles with the same angle measures can have different side lengths.
(c) To determine if a triangle can have side lengths 4cm, 3cm, and 8cm, we apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
4cm + 3cm > 8cm
4cm + 8cm > 3cm
3cm + 8cm > 4cm
Since all three inequalities are not satisfied (4 + 3 = 7 is not greater than 8, which is the longest side), it is not possible to form a triangle with these side lengths.
(d) To determine if a triangle can have side lengths 8cm, 15cm, and 17cm, we apply the triangle inequality theorem.
8cm + 15cm > 17cm
8cm + 17cm > 15cm
15cm + 17cm > 8cm
Since all three inequalities are satisfied, it is possible to form a triangle with these side lengths.
All such triangles are congruent, since these side lengths satisfy the conditions for a unique triangle known as a Pythagorean triple.
Hence, the triangle with side lengths 8cm, 15cm, and 17cm is a right triangle, and all right triangles with these side lengths are congruent by the Pythagorean theorem.
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The graph of polygon FGHI is shown. Graph the image of FGHI after a reflection across the line y=-1. Include the line of reflection. Then write the coordinates of the image.
The coordinates of the reflected polygon F'G'H'I' are as follows:
F'(-2, -1), G'(5, -4), H'(8, -5), and I'(6, -2).
What is the reflection?In mathematics, reflection is defined as the mirror image of a figure crossing a line (drawn or imagined), known as the line of reflection.
The vertices of the polygon FGHI are as follows:
F(2, -1)
G(5, 2)
H(8, 3)
I(6, 0)
To reflect the polygon FGHI across the line y = -1, we need to flip the points over the line.
Now we can reflect each of the points of the polygon across the line y = -1 to get the image:
F(2, -1) stays in the same place because it lies on the line of reflection.
G(5, 2) is reflected to G'(5, -4) by flipping it vertically across the line y = -1.
H(8, 3) is reflected to H'(8, -5), and
I(6, 0) is reflected to I'(6, -2).
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find the sine of angle C in this triangle.
The sine of angle C is √30/10.
Trigonometric ratios:Trigonometric ratios are mathematical expressions used to relate the angles and sides of a right-angled triangle.
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
are the fundamental ratios in a right-angle triangle
where
"Opposite" refers to the side opposite to the angle.
"Adjacent" refers to the side adjacent to the angle.
"Hypotenuse" refers to the longest side of the right-angled triangle
Here we have
A right-angle triangle DCB
Where DC = 10 units, CB = √70
From trigonometric ratios,
Sin θ = Opposite side/ Hypotenuse
Sin C = DB/CD
By the Pythagorean theorem
=> DC² = CB² + DB²
=> (10)² = (√70)² + DB²
=> 100 = 70 + DB²
=> DB² = 100 - 70
=> DB = √30
Sin C = √30/10
Therefore,
The sine of angle C is √30/10.
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Which expressions contain exactly two terms? Choose ALL that are correct. Responses −5+6x+3y2 − 5 + 6 x + 3 y 2 4x 4 x 7−9x 7 − 9 x (x+2)(y−4) ( x + 2 ) ( y − 4 ) 8x2+5x
The expression -5 + 6x + 3y2 has three terms, and the expression (x+2)(y-4) is a product of two factors, not a sum or difference of terms.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, without the use of equal sign (=). It can include one or more terms, which are separated by addition or subtraction operators.
The expressions that contain exactly two terms are:
7 - 9x
8x2 + 5x
Therefore, The expression -5 + 6x + 3y2 has three terms, and the expression (x+2)(y-4) is a product of two factors, not a sum or difference of terms.
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Find the maximum and the minimum value of the following objective function, and the value ofxandyat which they occur. the functionF=5y−4xsubject toy≤4x+1,y≥−4x+5, andx≤4The maximum value of the objective function is whenx=andy=
The maximum value of the objective function is 73 when x=4 and y=17 and minimum value is 21 when x=1 and y=5.
To find the maximum and minimum values of the objective function F=5y−4x, we need to use the constraints given in the question and solve for x and y. The constraints are y≤4x+1, y≥−4x+5, and x≤4.
First, we need to graph the constraints to find the feasible region. The feasible region is the area on the graph where all the constraints are satisfied.
Next, we need to find the corner points of the feasible region. The corner points are where the constraints intersect. The corner points are (1, 5), (4, 17), and (4, 11).
Finally, we need to plug in the corner points into the objective function to find the maximum and minimum values.
F(1, 5) = 5(5) - 4(1) = 21
F(4, 17) = 5(17) - 4(4) = 73
F(4, 11) = 5(11) - 4(4) = 47
The maximum value of the objective function is 73 when x=4 and y=17. The minimum value of the objective function is 21 when x=1 and y=5.
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A function is given. g(x)=3−4/5x; x=−5 ,x=4 (a) Determine the net change between the given values of the variable. (No Response) (b) Determine the average rate of change between the given values of the variable. (No Response)
A function is given. g(x)=3−4/5x; x=−5 ,x=4 the net change between the given values of the variable is -7.2. The average rate of change between the given values of the variable is -0.8.
(a) To determine the net change between the given values of the variable, we need to find the difference between the function values at x = -5 and x = 4.
g(-5) = 3 - 4/5(-5) = 3 + 4 = 7
g(4) = 3 - 4/5(4) = 3 - 3.2 = -0.2
Net change = g(4) - g(-5) = -0.2 - 7 = -7.2
(b) To determine the average rate of change between the given values of the variable, we need to find the slope of the secant line between the points (-5, 7) and (4, -0.2).
Average rate of change = (g(4) - g(-5))/(4 - (-5)) = (-7.2)/(9) = -0.8
Therefore, the average rate of change between the given values of the variable is -0.8.
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vIf the slope of a line is 32, how much vertical change will be present for a horizontal change of 96ft?
A horizontal change of 96ft, there will be a vertical change of 3072ft.
The slope of a line is the ratio of the vertical change to the horizontal change between two points on the line. In other words, the slope is the rise over the run.
If the slope of a line is 32, that means that for every 1 unit of horizontal change, there is a 32 unit vertical change.
So, if the horizontal change is 96ft, we can use the slope formula to find the vertical change:
Vertical change = slope × horizontal change
Vertical change = 32 × 96
Vertical change = 3072
Therefore, for a horizontal change of 96ft, there will be a vertical change of 3072ft.
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1. a) Indicar tres monomios semejantes a - 3x¹.
b) ¿Vo F? 12ab y -12ab son semejantes.
c) ¿Vo F? 2x²y y 2xy² son semejantes.
d) Escribir dos monomios semejantes de grado 5 y cuya parte literal conste de dos letras.
Answer:
a) -5x, 3x y 7x son monomios semejantes a -3x¹.
b) Verdadero, ya que ambos tienen coeficiente -12 y la misma parte literal ab.
c) Falso, ya que el primer monomio tiene exponente 2 en la variable x y exponente 1 en la variable y, mientras que el segundo monomio tiene exponente 1 en x y exponente 2 en y.
d) 3x²y³ y 2x²y³ son dos monomios semejantes de grado 5 y cuya parte literal consta de las variables x e y elevadas a exponentes 2 y 3 respectivamente.
A farmer sells 7.1 kilograms of apples and pears at the farmers market. 2 5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmers market?
answer:
4.6 kilograms of pears
question:
I don't know if you meant 2.5 or 25 but ill assume you meant 2.5
I need help on this asap!!!!!
If Emma needs to travel a distance of 15 miles or less, she should choose the red cab company because it has a lower cost. If she needs to travel more than 15 miles, she should choose the yellow cab company
Determining the company that minimizes cost
From the question, we are to determine which company Emma should use when she wants to minimize cost.
Let's assume that Emma needs to travel a distance of d miles to get to the airport.
The cost C of taking the red cab company can be represented by the function:
Cred(d) = 3.50 + 1.25d
Similarly, the cost C of taking the yellow cab company can be represented by the function:
Cyellow(d) = 5.00 + 1.15d
To determine which company Emma should use to minimize cost, we need to find the value of d that makes the cost of each company equal. In other words, we need to solve the equation:
Cred(d) = Cyellow(d)
Substituting the expressions for Cred(d) and Cyellow(d), we get:
3.50 + 1.25d = 5.00 + 1.15d
Simplifying and solving for d, we get:
0.10d = 1.50
d = 15
Hence, if Emma needs to travel a distance of 15 miles or less, she should choose the red cab company because it has a lower cost. If she needs to travel more than 15 miles, she should choose the yellow cab company.
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What is the constant of proportionality between
�
yy and
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xx in the graph?
The response to the given question would be that The slope of the line is the constant of proportionality if the graph is a straight line through the origin.
what is proportionality?Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.
It is difficult to estimate the constant of proportionality between two variables, y and x, without first viewing the graph.
Nevertheless, the constant of proportionality may be calculated by dividing any y-value by its corresponding x-value if the two variables are directly proportional, which means that when x rises, y rises as well at a consistent pace.
If y = kx, where k is the proportionality constant, then mathematically, k = y/x at every point on the graph.
The slope of the line is the constant of proportionality if the graph is a straight line through the origin.
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1. A wholesaler received a shipment of goods, which is reported to be containing at most 2% defective items. He will accept the shipment if the claim is found true and reject if the percentage of defective items is more. To verity this claim, he draws a sample of 200 items and finds that 10 items are defective. Use 5% level of significance to investigate the claim.
At a 5% level of significance, the claims that a shipment of goods contains at most 2% defective items is accepted.
To investigate the claim that the shipment contains at most 2% defective items, we can use the 5% level of significance. The claim is that the population proportion of defective items is at most 2%, or p0 ≤ 0.02. The sample size is n = 200, and the sample proportion of defective items is pobs = 10/200 = 0.05.
The test statistic is then:
z = (pobs - p0) / √(p0(1-p0) / n)
= (0.05 - 0.02) / √(0.02(1-0.02)/200)
= 1.02.
With a 5% level of significance, we can look up the critical value for a one-tailed z-test and find that it is zα/2 = 1.645. Because 1.02 < 1.645, the test statistic is not greater than the critical value, and thus we fail to reject the null hypothesis that the population proportion of defective items is at most 2%.
In conclusion, with a 5% level of significance, the claim that the shipment contains at most 2% defective items is accepted.
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If f (x) = √x
Write the equation for the transformed functions "y1" and "y2"
y1 = 2f (x + 5) -3 Equation : _______
y2 = f(2(x - 5)) + 3 Equation : _______
Given the equation f(x) = x^2 - 9, write the equations for – f(x) and for f(–x)
f(x) = x^2 - 9
f(-x) = (-x)^2 - 9
y1 = 2√(x + 5) - 3
y2 = √(2(x - 5)) + 3
For the second question:
f(x) = x^2 - 9
f(-x) = (-x)^2 - 9
f(-x) = x^2 - 9
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