The radius of a circle is 7 inches the radius of circle, B is 3inches greater than the radius of circle A. If the radius of circle C is 4 inches greater than the radius of circle B the radius of circle D is 2 inches less than the radius of circle C, see what is the area of each circle
The area of each circle would be given below:
Circle A= 153.86 in²
Circle B = 314in²
Circle C = 615.44in²
Circle D = 452.16 in²
How to calculate the area of circle?To calculate the area of a circle, the formula that should be used is given below such as follows:
Area of circle = πr²
For circle A;
radius = 7 in
area = 3.14×7×7 = 153.86 in²
For circle B;
radius = 3+7 = 10in
area = 3.14×10×10 = 314in²
For circle C;
radius = 10+4 = 14 in
area = 3.14×14×14
= 615.44in²
For circle D;
radius = 14-2 = 12in
radius = 3.14×12×12
= 452.16 in²
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Given u = - i + j v = 8i - 2j and w = - 4j find pro*j_{u}(v + w)
The projection of (v + w) onto u is (-8 √(2)i + 6 √(2)j).
Now, let's consider the given vectors u = - i + j, v = 8i - 2j, and w = - 4j. The question asks us to find the projection of vector v + w onto the vector u, denoted as proj_u(v + w). To find this projection, we need to use the dot product between the two vectors.
First, we need to calculate v + w, which is (8i - 2j) + (-4j) = 8i - 6j. Next, we calculate the dot product of u and (v + w):
u · (v + w) = (-i + j) · (8i - 6j)
= -8i + 6j - 8i + 6j
= -16i + 12j
The dot product measures the similarity between two vectors, and in this case, it gives us the component of (v + w) that is parallel to u. To find the projection of (v + w) onto u, we need to divide this component by the magnitude of u:
proj_u(v + w) = (u · (v + w)) / ||u||
= (-16i + 12j) / √(2)
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a 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm
The shaded area of the portion as shown in the diagram is 78.04 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the shaded area of the portion, we use the formula below
Formula:
A = πr²-lw.................. Equation 1Where:
A = Area of the shaded portionr = Radius of the circlel = Length of the rectanglew = Width of the rectangleFrom the question,
Given:
r = 6 cml = 7 cmw = 5 cmSubstitute these values into equation 1
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Complete question: A 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm. Calculate the area of the shaded portion.
The mean daily demand for water, in millions of gallons, in a local city is 300, with a standard deviation of 30. Every morning the water treatment plant produces 380 million gallons of water. What is the probability that the water will run out on a given day, if the mean daily demand of water is normally distributed?
The probability that the water will run out on a given day is 0.0038.
What is the probability that water will run out?To find the probability that the demand for water on a given day exceeds the supply of 380 million gallons, we use the standard normal distribution to standardize the value of 380 million gallons as follows:
z = (x - µ) / σwhere;
x = of 380 million gallons,
µ is the mean daily demand of water = 300 million gallons,
σ is the standard deviation = 30 million gallons.
Substituting the given values:
z = (380 - 300) / 30
z = 2.67
Using a calculator, the probability that a standard normal random variable is greater than 2.67 is 0.0038.
Therefore, the probability that the water will run out on a given day is 0.0038.
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Solids A and B are similar. Use the given information and scale factor k from solid A to solid B to find the surface area of solid B.
Prism A has a surface area of 805 square feet and the and k=1/5
Answer:
32.2 ft²---------------------
We know that area is the product of two dimensions.
Hence we consider the square of the scale factor when comparing areas of similar figures.
The surface area of solid B is k² times the surface area of solid A:
S(B) = k²S(A)Substitute and calculate:
S(B) = (1/5)²(805) = 805/25 = 32.2 ft²Solve the equation x2 = 8.
x = 4
x = ±4
x = 8‾√
x = ±8‾√
Answer:
Step-by-step explanation:
x^2 = 8
x=+-√8
36 is 15% of what number
7
35cm
42cm
X =
6cm
cm
N
HELP ME FAST GUYS!! Asap
The value of x in the polygon is 5 centimetres.
How to find the side of similar polygon?A polygon is a two-dimensional geometric figure that has a particular number of sides.
Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio .
Therefore, using the ratio of the similar polygon, let's find the value of x as follows:
35 / x = 42 / 6
cross multiply
35 × 6 = 42x
210 = 42x
divide both sides of the equation by 42
x = 210 / 42
x = 5 cm
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Help please!!!!
Whoever answers right gets brainliest!
When w = 10 and z = 2, the value of expression 2w⁻²z⁰ is equal to 1/50. So, correct option is A.
The expression 2w⁻²z⁰ can be simplified as follows:
2w⁻²z⁰ = 2/w² * z⁰
Since z⁰ = 1 for any non-zero value of z, we can simplify further:
2w⁻²z⁰ = 2/w² * 1
Now we can substitute w = 10 into the expression:
2(10)⁻² * 1 = 2/100 = 1/50
In general, when we have a negative exponent in an expression, we can rewrite it as a positive exponent in the denominator. In this case, w⁻² can be rewritten as 1/w². Additionally, any number raised to the power of 0 is always 1, so z⁰ = 1. By simplifying the expression, we can easily substitute the given values of w and z to evaluate the expression.
So, correct option is A.
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Which of the following is an exponential equation?
A.
3x + 2 = 23
B.
5 ‒ x2 = 4
C.
3x + 2 = 23
D.
7 ‒ 0.5x = 2x
Answer:
a. 3x = 23-2
3x = 21
x = 21÷3
x = 7
b. 5x - 2 = 4
5x = 4+2
5x = 6
x = 6÷5
x = 1.2
c. 3x = 23-2
3x = 21
x = 21÷3
x = 7
d. 7 = 2x+0.5x
7 = 2.5
x = 2.5÷7
x = 2.8
Of all the registered automobiles in Colorado, 5% fail the state emissions test. Ten automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places.
The probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.
what is binomial distribution?The number of successes in a certain number of independent trials is modelled by the binomial distribution, which has just two potential outcomes for each trial, commonly referred to as "success" and "failure."
We can solve this problem by using the binomial distribution formula:
[tex]P(X=k) = (n\ choose\ k) * p^k * (1-p)^{(n-k)[/tex]
where:
P(X=k) is the probability of getting exactly k automobiles that fail the emissions test
n is the number of automobiles being tested, in this case, n = 10
k is the number of automobiles that fail the emissions test
p is the probability of a single automobile failing the emissions test, in this case, p = 0.05
Using this formula, we can calculate the probability of getting exactly k failures for k = 0, 1, 2, ..., 10, and then add up these probabilities to get the probability of getting at least one failure.
The probability of getting exactly k failures is:
[tex]P(X=k) = (10\ choose\ k) * 0.05^k * 0.95^{(10-k)[/tex]
Using a calculator or statistical software, we can calculate these probabilities:
[tex]P(X=0) = (10 choose 0) * 0.05^0 * 0.95^10 = 0.5987\\P(X=1) = (10 choose 1) * 0.05^1 * 0.95^9 = 0.3151\\P(X=2) = (10 choose 2) * 0.05^2 * 0.95^8 = 0.0746\\P(X=3) = (10 choose 3) * 0.05^3 * 0.95^7 = 0.0119\\P(X=4) = (10 choose 4) * 0.05^4 * 0.95^6 = 0.0013\\P(X=5) = (10 choose 5) * 0.05^5 * 0.95^5 = 0.0001\\[/tex]
[tex]P(X=6) = (10 choose 6) * 0.05^6 * 0.95^4 = 0.0000\\P(X=7) = (10 choose 7) * 0.05^7 * 0.95^3 = 0.0000\\P(X=8) = (10 choose 8) * 0.05^8 * 0.95^2 = 0.0000\\P(X=9) = (10 choose 9) * 0.05^9 * 0.95^1 = 0.0000\\P(X=10) = (10 choose 10) * 0.05^10 * 0.95^0 = 0.0000\\[/tex]
The probability of getting at least one failure is:
[tex]P(X > =1) = 1 - P(X=0) = 1 - 0.5987 = 0.4013[/tex]
Therefore, the probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.
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The slope of the line whose equation is 5x - 3y = 4 is 4/5 5/3 -3/5
The slope of the relation with the equation 5x - 3y = 4 is 5/3
Calculating the slope of the relationTo find the slope of the line whose equation is 5x - 3y = 4, we need to rearrange the equation to be in slope-intercept form, y = mx + b, where m is the slope of the line.
First, we'll subtract 5x from both sides:
-3y = -5x + 4
Next, we'll divide both sides by -3 to isolate y:
y = (5/3)x - 4/3
Now we can see that the slope of the line is 5/3.
So the correct answer is: 5/3
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For the right triangle shown below, find the exact values of:
sinB b)tanA c)cosA
Answer:
17
Step-by-step explanation:
11+6=17
(a) The exact value of sin B is 6 / 12.53
(b) The exact value of tan A is 11 / 6
(c) The exact value of cos A is 6 / 11
What is the value of sin (B) , tan (A) and cos (A)?The value of sin (B), cos (A) and tan (A) is calculated by applying trigonometry ratio as follows;
The trigonometry ratio is simplified as;
SOH CAH TOA;
SOH ----> sin θ = opposite side / hypothenuse side
CAH -----> cos θ = adjacent side / hypothenuse side
TOA ------> tan θ = opposite side / adjacent side
The value of the hypotenuse side of the right triangle is;
L = √ (6² + 11²)
L = 12.53
(a) The exact value of sin B is;
sin B = 6 / 12.53
(b) The exact value of tan A is;
tan A = 11 / 6
(c) The exact value of cos A is;
cos A = 6 / 11
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Mariana is making a large pot of pasta. She mixes together 518 pounds of pasta, 6 pounds of sauce, and 478
pounds of onions.
To find out how many 12
pound servings can she make, which two equations would you need?
A.
518+478+6=16
B.
518+478−6=4
C.
4÷12=8
D.
16÷12=32
E.
16×12=8
We need to use equations C and D:
C. 4 ÷ 12 = 1/3
D. 16 ÷ 12 = 4/3
To find out how many 12-pound servings Mariana can makeWe need to divide the total amount of pasta by 12. Therefore, we need to use equations C and D:
C. 4 ÷ 12 = 1/3
D. 16 ÷ 12 = 4/3
Equation C shows that each serving is 1/3 of a pound
Equation D shows that Mariana can make 4/3 servings
Therefore, Mariana can make 4/3, or approximately 1.33, servings of 12 pounds each.
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Y=-10x+1 with x being -5
Answer:
Y=-10x+1 with x being -5
y = -10 *-5 +1
y = -50+1
y =-49
e=? image attached please help
Answer:
e = 3
Step-by-step explanation:
Use the property of the proportion to find e (cross-multiply):
[tex]10 \times e = 6 \times 5[/tex]
[tex]10e = 30[/tex]
Divide both sides of the equation by 10 to make e the subject:
[tex]e = 3[/tex]
Answer:
3
Step-by-step explanation:
6 x 10 = 60
6 x 5 = 30
5/10 = 30/60
30/ 10= 3
60/ 10 = 6
E/6 = 3/6
E=3
Which of the following are solutions to the system of inequalities y<−x+5 and y≥3x+1?
A)
(1,0)
cross out
B)
(−2,2)
cross out
C)
(1,6)
cross out
D)
(0,1)
cross out
E)
(1,4)
cross out
F)
(−2,7)
From the graph attached below, the solution to the system of linear inequalities are (1, 4)
What is the solution to the system of linear inequalities?A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.
In the problem given;
y < - x + 5 ...eq(i)
y ≥ 3x + 1 ...eq(ii)
To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.
From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E
Kindly find attached graph below
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Tamika is seeking a loan with a simple
The interest that Tamika will be charged in interest after 24 months of borrowing $5,000 at 8% simple interest per year is $800.
What is simple interest?Simple interest is the interest system that computes interest only on the principal for each period.
Unlike the compound interest system, simple interest does not charge interest on accumulated interest and the principal.
The principal loan amount borrowed by Tamika = $5,000
The interest rate per year = 8%
The loan period = 24 months = 2 years (24/12)
Simple Interest = Principal x Rate x Period
= $800 ($5,000 x 8% x 2)
Thus, for borrowing $5,000 for 24 months of 2 years, Tamika would pay a simple interest of $800.
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Complete Question:Tamika is seeking a loan with a simple interest rate of 8% per year. If she wants to borrow $5,000, then how much will she be charged in interest after 24 months?
Julieta says that it is not possible to draw a quadrilateral that is not a trapezoid and a parallelogram. Is Julieta correct explain why or why not.
Julieta's claim about the quadrilateral is false.
How to prove or disprove Julieta claim?The statement is given as:
It is impossible to draw a quadrilateral that is not a trapezoid and not a parallelogram.
The condition for a shape to be a quadrilateral is that the shape must have four sides.
An irregular shape that has four sides is a quadrilateral, but neither a quadrilateral nor a parallelogram
Therefore, Julieta's claim is false
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find the missing sides of this triangle (Hint: is this a special right triangle?)
(10 on the adjacent and two 45° angles on both ends if anyone can’t see)
Answer:
Both sides are equal, and are equvalent to 5 square root of 2
Step-by-step explanation:
This is a special right angled triangle known as the 45-45-90 triangle
The hypotenuse of a 45-45-90 triangle is x square root 2, with x being both sides of the triangle
10=x square root of 2 (Divide both sides by square root of 2)
10/square root of 2=x (Rationalize)
x=5 square root of 2
The current of a river is 2 miles per hour. A boat travels to a point 15 miles upstream and back in 4
hours. What is the speed of the boat in still water?
Using the relationship of distance, time and speed, the speed of the boat in still water is 8mi/hr
What is the speed of the boat in still water?To determine the speed of the boat in still water, we can write an equation to represent this.
The speed as it travels upstream = x - 2
The speed as it travels downstream = x + 2
The total distance travelled by the boat = 15 + 15 = 30mi
Let's write an equation to represent this;
15/(x - 2) + 15/(x + 2) = 4
simplifying this;
15(x + 2) + 15(x - 2) = 4(x - 2)(x + 2)
15x + 30 + 15x - 30 = 4x² - 16
30x = 4x² - 16
4x² - 30x - 16 = 0
Solving for x;
x = -0.5, 8
But since the speed can't be negative, the speed is 8 mi/hr
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Given u=12i-3j and v=-5i+11j, what is u x v?
Answer:
117
Step-by-step explanation:
You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).
Cross productThe cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.
u×v = (12)(11) -(-3)(-5) = 132 -15
u×v = 117
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Write a slope-intercept equation for a line passing(3,-2) through the point that is parallel to the line 3X+4Y= 9. Then write a second equation for a line passing through the point (3,-2) that is perpendicular to the line 3X+4Y= 9.
Why does income for a family tend to go up when two single persons marry?
A. Newly married couples tend to have two earners.
B. Married people work longer hours than single people.
C. Two people can live as cheaply as one.
D. The Federal government's marriage tax favors married people.
Answer:
A.) Newly married couples tend to have two earners.
Step-by-step explanation:
When newly married couples first start off marriage, they tend to both work to make stable income since they recently had to work to make money for only their selves, which is why they both tend to have two earners.
Based on the scenario, determine if it would be better to use the mean or median to describe the data set.
1 Workers at a plant are trying to show that they work too many hours. There are five part-time workers along with ten full time workersWhat summary statistic would best defend their position?
2Mrs. Smith is trying to show that her class did really well on the last test. She has four students that should have been in honors mathbut instead stayed in regular math. What summary statistic should she use to defend her position?
3. A CEO is trying to determine the average salary of his workersHe has some workers that work part- time and some very highly paid workersIf he wants a true idea of the average salarywhat summary statistic should he use?
4. Henry is trying to determine his average test grade in a class. All of his grades have been within five points of each other. He needs the average in order to calculate his overall gradeWhat summary statistic should he use?
____median
____median
____mean
____mean
1. It would be better to use the median to describe the data set.
2. It would be better to use the median to describe the data set.
3. It would be better to use the mean to describe the data set as the average salary of the workers is to be calculated.
4. It would be better to use the mean to describe the data set as the average test grade of the class is to be calculated.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
A. x² + (y - 3)² = 36.
D. x² + (y + 8)² = 36.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = diameter/2 = 12/2 = 6 units.
Center, (h, k) = (0, 3).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 6²
x² + (y - 3)² = 36.
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The table below represents a linear equation
Which function has a greater slope and greater y-intercept than the linear function represented in the table?
A. y = 2x + 8.5
B. y = 3x +7.5
C. y = 5x + 6.5
D. y = 10x + 5.5
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
We have to given that;
The table below represents a linear equation.
Now, The equation of line is,
Take two points (- 1, 5) and (1, 9)
⇒ y - 5 = (9 - 5) / (1 + 1) (x + 1)
⇒ y - 5 = 4/2 (x + 1)
⇒ y - 5 = 2 (x+ 1)
⇒ y - 5 = 2x + 2
⇒ y = 2x + 7
Hence, By options,
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
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if you divide 781.253 by 100, what will be the place value of 2
Answer:
When you divide 781.253 by 100, you get 7.81253 as the result.
The digit 2 is in the hundredths place in the dividend 781.253. Since we are dividing by 100, which has two decimal places, we move the decimal point two places to the left in the dividend to get the quotient.
Therefore, the digit 2 is in the ten-thousandths place in the quotient 7.81253.
During an experiment, 2 mL of solution evaporates from a beaker each minute. After 5 minutes, there are 50.25 ml of the solution remaining. Write an equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment.
An equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment is y = 9.65x + 2.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (50.25 - 2)/(5 - 0)
Slope (m) = 48.25/5
Slope (m) = 9.65.
At data point (0, 2) and a slope of 9.65, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 9.65(x - 0)
y = 9.65x + 2
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what does scaled version mean in this case its 3:5 scaled version but i just want to know what it means asap please help
Scaled version means adjusted value from the original size. For example, 3:5 could be a scaled version of 6:10.
Understanding Scale VersionScale Version of an object is a replica or model of the original object that has been proportionally reduced or enlarged in size. The scale of a model is the ratio of the size of the model to the size of the original object. For example, if a model of a building is one-tenth the size of the actual building, then the scale of the model is 1:10, which means that every measurement on the model is one-tenth of the corresponding measurement on the actual building.
Scale versions of objects are often used in engineering, architecture, and design to create smaller or larger versions of objects that can be studied, tested, or used for other purposes. For example, architects might create scale models of buildings to study their design and appearance, while engineers might create scale models of machines or structures to test their performance under different conditions.
Scale versions can also be used in maps, where the scale is used to indicate the relationship between the size of the map and the size of the area it represents. In this case, the scale might be represented as a ratio, such as 1:10,000, or as a statement of the size of a unit of measurement on the map, such as 1 inch equals 1 mile.
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