Answer:
7/25
Step-by-step explanation:
0.28 = 28/100 = 7/25
Find the probability that a point chosen at random would lie in the shaded area of the figure. Round to the nearest tenth of a percent.
with the steps and explanation
Answer:
Step-by-step explanation:
The required probability is simply the (shaded area)/(area of the whole box)
The area of the whole box would be:
6r*2r = 12 r^2
The shaded area is tough to calculate, but you can get the
white area instead.
The left hole (white area) consists of a semi-circle and a rectangle.
The center hole is a circle.
The right hole (white area) consists of a semi-circle and a rectangle.
The 2 semi-circles in the left and right hole combine to be a circle.
The 2 rectangles in the left and right hole combine to be a square.
The total area of holes are:
(area of circle)*2 + (area of square) ### 2 circles 1 square in total
=r^2*pi*2 + (2r)^2
=r^2*pi*2 +4*r^2
then we can get the shaded area by:
(area of the whole box) - (The total area of holes)
= 12 r^2 - (r^2*pi*2 +4*r^2)
=8*r^2 - r^2*pi*2
Finally:
(shaded area)/(area of the whole box)
=(8*r^2 - r^2*pi*2)/(12 r^2)
=(8-pi*2)/(12)
=0.143067891
=14.3% (corr. to 3 sig. fig.)
What is the increase in Fahrenheit temperature if the Celsius temperature increases by 7°?!
The increase in Fahrenheit temperature is of 12.6 degrees.
What is the increases in Fahrenheit temperature?The formula to have a change of units is:
To convert Celsius to Fahrenheit, you can use the formula:
°F = (°C x 1.8) + 32
(So you are correct, the rate is 9/5 = 1.8)
The increase of 7°C wold be given by the difference:
increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32
Solving that equation we can see that
increase = 12.6°F
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Answer:
he increase in Fahrenheit temperature is of 12.6 degrees.
What is the increases in Fahrenheit temperature?
The formula to have a change of units is:
To convert Celsius to Fahrenheit, you can use the formula:
°F = (°C x 1.8) + 32
(So you are correct, the rate is 9/5 = 1.8)
The increase of 7°C wold be given by the difference:
increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32
Solving that equation we can see that
increase = 12.6°F
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Step-by-step explanation:
Geometry I need help
Figure O is reflected followed by a translation of 4 units in the left direction.
Given that:
Figure O and Figure P are shown on the graph.
The translation does not change the shape and size of the geometry. But changes the location.
Figure O is translated leftward by 4 units.
The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.
The translated figure O is reflected across the x-axis.
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Analyze the diagram below and complete the instructions that follow.
8
45°
Find the value of x.
A. 4
B. 8√√2
2
C. 4√2
DG
45°
Save and Exit
Next
Subr
Answer:
Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.
Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:
x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)
So the value of x is option B: 8√2 / 2 or simplified, 4√2.
Area/ Perimeter question. Any help? i have an assignment to complete.
Answer:
13 + 8 + 13 + (1/2)(8π) = 34 + 4π feet
= 46.57 feet
What's this answer?
2 5/6 • -3 2/4 =
Answer:
-9 11/12
Step-by-step explanation:
You want the product of 2 5/6 and -3 2/4.
ProductThe product of mixed numbers is often most easily computed by rewriting them to improper fractions.
(2 5/6)(-3 2/4) = (17/6)(-7/2) = -(17·7)/(6·2) = -119/12
= -(108/12 +11/12)
= -9 11/12
__
Additional comment
Your calculator can probably help you with this.
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4. Malaki has a 'no interest-free period' credit card that charges 16.5% p.a. interest. On 9 January he purchases a phone costing K395.00. His January statement is dated 28 January and the phone is the only item on it.
a. How much interest is charged on the January credit card statement?
b. Malaki pays K100.00 off the amount owed on 28 January and makes no more purchases or payments before the next credit card statement arrives on 28 February. How much will this statement show that Malaki owes?
Answer:
K5.60.
Step-by-step explanation:
a circle has a diameter of 30 inches and an area of approximately 675 square inches.If the diameter of circle increa to 60 inches, what would be an approximation of the new area?
Answer:
If the diameter of the circle increases to 60 inches, the new area would be approximately 2700 square inches.
1. Your utility company charges 10 cents per kilowatt hour of electricity. Complete parts (a) and (b) below.
a) What is the daily cost of keeping a 100-watt light bulb lit for 5 hours each day?
Answer:
b) How much will you save in a year if you replace the bulb with an LED that provides the same amount of light using only 26 watts of power? Round your answer to the nearest cent.
Answer:
1. Daily cost of keeping the bulb lit for 5 hours is 5 cents.
2. Switching to an LED bulb could save $13.50 in a year.
What is costs of running a 100-watt light bulb?Power consumed by the 100-watt bulb in 5 hours is:
= 100 watts x 5 hours
= 500 watt-hours
= 0.5 kilowatt-hours
The cost of electricity for 0.5 kilowatt-hours at a rate of 10 cents per kilowatt-hour is:
= 0.5 kWh x 10 cents/kWh
= 5 cents
b. The power consumed by the 26-watt LED bulb over 5 hours is:
= 26 watts x 5 hours
= 130 watt-hours
= 0.13 kilowatt-hours
The cost of electricity for 0.13 kilowatt-hours at a rate of 10 cents per kilowatt-hour is:
= 0.13 kWh x 10 cents/kWh
= 1.3 cents
Annual savings is:
= (Daily cost 100-watt bulb - Daily cost LED bulb) * 365 days
= (5 cents - 1.3 cents) x 365 days
= $13.50.
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what is the maths formula for area
Answer:
Quick internet search:
Vanessa runs 4 miles each week. Use the number line below to solve and represent the number of weeks it will take her to run 96 miles.
The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks
How to calculate the number of weeks used by Vanessa for race?The amount of distance that Vanessa covers for a week = 4 miles
The amount of weeks it will take for her to cover 96 moles would be = ?
That is;
1 week = 4 miles
X weeks = 96 miles
Make X the subject of formula;
X = 96× 1/4
= 24 weeks
Therefore Vanessa will be able to cover 96 miles in only 24 weeks.
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Solve the problem. At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The results are given in the table below. At the 0.05 significance level, test the hypothesis that the proportion of wins is the same for teams wearing suits as for teams wearing jeans. Suit- win= 22 loss=28 t-shirt win= 28 loss=22 . Answer Choices : A.df=4, B.df=1,C.df=2,df=3.
At the 0.05 significance level, the degree of freedom is 1. So, correct option is B.
To test the hypothesis that the proportion of wins is the same for teams wearing suits as for teams wearing jeans, we can use the chi-square test for independence. The null hypothesis is that the proportion of wins is the same for both groups, and the alternative hypothesis is that they are different.
Using the given data, we can calculate the expected frequencies under the assumption of equal proportions of wins for both groups. The expected frequency for each cell is given by (row total x column total) / grand total.
The calculated chi-square statistic is 2.667, and the degrees of freedom are (r-1)(c-1) = (2-1)(2-1) = 1.
Using a chi-square distribution table with 1 degree of freedom and a significance level of 0.05, the critical value is 3.84. Since the calculated chi-square value is less than the critical value, we fail to reject the null hypothesis.
Therefore, we can conclude that there is not enough evidence to suggest that the proportion of wins is different for teams wearing suits versus jeans and t-shirts at the 0.05 significance level.
The answer choice that corresponds to 1 degree of freedom is B
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freddy drew a plan for a rectangular piece of material that he will use for a blanket. the three of the vertices are (-2, -3), (-2.3,1.6), (4.6,1.6). what are the coordinates of the fourth vortex?
The coordinates of the fourth vortex of the rectangular piece of material drawn by Freddy would be (4. 6, - 3 ).
How to find the fourth vortex ?Rectangles are quadrilaterals which have two sets of parallel lines. This means that two sets of sides are equal which are the opposite ones. This means that when plotted on a coordinate plane, of the four points, the x - values should repeat twice and the y - values should repeat twice as well.
They would do so by alternating with each other. This means that in a rectangle with (-2, -3), (- 2 . 3, 1 . 6), ( 4 . 6 , 1. 6 ), the fourth vertex would be the two x and y values that are yet to repeat which would be:
( 4. 6, - 3 ).
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You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
The coordinate of the point after transformation is: (3, -4)
What is the coordinate after moving of point?The coordinate initially is given as (0, -4).
Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:
(0 - 1, -4)
= (-1, -4)
Moving by 4 units to the right means an addition of 4 units to x coordinate to get:
(-1 + 4, -4)
= (3, -4)
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I don’t understand my head actually hurts from this
Answer:
AB = 90° , AC = BC = 135°
Step-by-step explanation:
the arc AB is equal to the measure of the central angle it subtends, then
AB = 90°
the sum of the arcs in a circle = 360° , then since AC and BC are congruent
AB + AC + BC = 360° ( since AC = BC ), then
90° + 2AC = 360° ( subtract 90° from both sides )
subtract 90° from both sides
2AC = 270° ( divide both sides by 2 )
AC = 135°
since AC = BC , then
AC = BC = 135°
which point is on the line 4y-2x=0
Answer:
(2,1)
Step-by-step explanation:
The line 4y - 2x = 0 can be written in slope-intercept form as y = 1/2x.
So any point that satisfies this equation will lie on the line. For example, the point (2,1) satisfies the equation:
4(1) - 2(2) = 0
So the point (2,1) is on the line.
Derek made a quilt for his cousin's doll. The quilt had a 7 × 7 array of different color square patches. If each patch is 1 _ in long, what is the area of the whole quilt? *
2401/16 square inches
Step-by-step explanation:
Given:
The quilt made by Spencer had a 7×7 array of different color square patches such that each patch is in long.
To find: the area of the whole quilt
Solution:
Side of each quilt =
Quilt is in the form of a square such that area of square is given by
Therefore, area of quilt = square inches
Laura is 3 ft tall how tall is Laura in inches
HELP DUE IN 30 MINUTES! I have an ice cream cone that has a radius of 1in and a height of 3in. How can you find how much ice cream could fit in the cone?
Answer:
Step-by-step explanation:
just do how tall times the diamiter divided by the
What is the range of this function?
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining.
A 2-column table with 4 rows. The first column is labeled x with entries 0, 0.5, 1, 1.5. The second column is labeled y with entries 40, 39.25, 38.5, 37.75.
If the Raj’s bathtub is draining at rate of 1.5 gallons of water per-minute, then the range will be (c) all real numbers such that 0 ≤ y ≤ 40.
The "Range" of function is defined as the set of all possible "output-values'.
The amount of water remaining in the bathtub is decreasing as it drains, so the range of the function is bounded below by 0 (because we cannot have negative water in the bathtub) and above by 40 (the initial amount of water in the bathtub).
Looking at the given values of y, we can see that the value of "y" lies between 0 and 40.
Therefore, the correct option is (c).
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The given question is incomplete, the complete question is
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining.
x y
0 40
0.5 39.25
1 38.5
1.5 37.75
What is the range of this function?
(a) all real numbers such that y ≤ 40
(b) all real numbers such that y ≥ 0
(c) all real numbers such that 0 ≤ y ≤ 40
(d) all real numbers such that 37.75 ≤ y ≤ 40.
What transformation maps the pre-image (red) onto the image (blue)?
translation
rotation
reflection
glide reflection
Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed.
The 99% confidence interval for the population proportion p is (0.776, 0.824).
To find the 99% confidence interval for a proportion, we can use the formula:
CI = p^ ± z*(SE)
where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.
For a 99% confidence interval, the critical value z is 2.576.
Substituting the given values into the formula, we have:
CI = 0.80 ± 2.576*(0.03/√200)
Simplifying this expression, we have:
CI = 0.80 ± 0.024
This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.
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Use cramers rule to solve the system below
2x -3y = -8
4x + 3y = -34
A) Let A be to coefficient matrix, fill in matrix a below
b) Find the determinant of matrix A.
C) Let Matrix X be the matrix used to solve for the x variable. Write this matrix below
D) find the determinant of matrix X
E) Let Matrix Y be the matrix used to solve for the 'y' variable. Write this matrix below:
F) find the determinant of matrix y
G) write your solution to the system above as a coordinate
The solution to all parts from a to f is shown below.
A) Matrix A:
[ 2 -3 ]
[ 4 3 ]
B) The determinant of matrix A is:
det(A) = (2*3) - (-3*4) = 6 + 12 = 18
C) Matrix X:
[ -8 -3 ]
[ -34 3 ]
D) The determinant of matrix X is:
det(X) = (-8*3) - (-3*-34) = -24 - 102 = -126
E) Matrix Y:
[ 2 -8 ]
[ 4 -34 ]
F) The determinant of matrix Y is:
det(Y) = 2(-34) - (-8) (4) = -68 + 32 = -36
G) Using Cramer's rule, we can solve for x and y as follows:
x = det(X) / det(A) = -126 / 18 = -7
y = det(Y) / det(A) = -36 / 18 = -2
Therefore, the solution to the system is (-7, -2).
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Which of the following is the inverse of G(t) if G(t) = 7(t - 4)?
G^-1(t)=t/7+4
G^1(t)=7t-4
G^-1(t)=t/7-4
G^-1(t)=7(t+4)
Answer:
G^-1(t)=t/7+4
Step-by-step explanation:
G(t) = 7(t - 4)
y = 7(x - 4)
x = 7(y - 4)
x/7 = y - 4
y = x/7 + 4
G^-1(t) = t/7 + 4
Answer: G^-1(t)=t/7+4
What is a name for the marked angle?
Slope of secant line pre calc
For the function f(x) = -2x² + 5x + 7 the slope of the secant line between x = -3 and x = 5 is -4
Consider the function f(x) = -2x² + 5x + 7
We need to find the slope of the secant line between x = -3 and x = 5
We know that the slope of secant line for the function f(x) on the interval [a, b] is given by the formula,
m = [f(b) - f(a)] / (b - a)
Let [a, b] = [-3, 5]
For x = -3 the value of the function would be,
f(-3) = -2(-3)² + 5(-3) + 7
= -2(9) - 15 + 7
= -18 - 15 + 7
= -26
And the value of the function for x = 5 would be,
f(5) = -2(5)² + 5(5) + 7
= -2(25) - 25 + 7
= -50 - 15 + 7
= -58
Using above formula the slope would be,
m = [f(5) - f(-3)] / (5 - (-3))
m = [-58 - (-26)] / 8
m = (-58 + 26) / 8
m = -4
Thus, the required slope is -4
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Answer:
Slope = 1
Step-by-step explanation:
A secant line is a straight line that intersects a curve at two or more points.
Given a curve represented by a function f(x), a secant line is determined by choosing two distinct points on the curve, (x₁, f(x₁)) and (x₂, f(x₂)).
The secant line passes through these two points and can be represented by a linear equation in the form y = mx + b, where m is the slope of the secant line and b is the y-intercept.
The slope of the secant line between the points (x₁, f(x₁)) and (x₂, f(x₂)) is given by the formula:
[tex]m = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]
To find the slope of the secant line between x = -3 and x = 5 for the function f(x) = -2x² + 5x + 7, first find f(-3) and f(5).
[tex]\begin{aligned}f(-3)&=-2(-3)^2+5(-3)+7\\&=-2(9)-15+7\\&=-18-15+7\\&=-26\end{aligned}[/tex]
[tex]\begin{aligned}f(5)&=-2(5)^2+5(5)+7\\&=-2(25)+25+7\\&=-50+25+7\\&=-18\end{aligned}[/tex]
Input the values into the slope formula:
[tex]m = \dfrac{f(5) - f(-3)}{5 - (-3)}=\dfrac{-18-(-26)}{5+3}=\dfrac{8}{8}=1[/tex]
Therefore, the slope of the secant line between x = -3 and x = 5 is 1.
The fucntion F is defined by f(x) =12/x +1/2. Find each value of th e fucnction. F(3)
The function f(x) = 12/x + 1/2 is given. To find f(3), we substitute x=3 in the function expression and simplify: f(3) = 12/3 + 1/2 = 4 + 0.5 = 4.5. Therefore, the value of the function f at x=3 is 4.5.
To find f(3) for the function f(x) = 12/x + 1/2. Start with the given function f(x) = 12/x + 1/2. Replace x with 3: f(3) = 12/3 + 1/2. Simplify the first term: 12/3 = 4
Add the two terms: f(3) = 4 + 1/2
Convert the mixed number to an improper fraction: 4 + 1/2 = 8/2 + 1/2 = 9/2
Simplify the fraction: 9/2 = 4 1/2
So, f(3) = 4 1/2 or 9/2, depending on the desired form of the answer.
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Determine whether the statement below is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
logb (x3 + y3) = 3 logb x + 3 logby
Using rules for logarithms we can see that the statement is false.
Is the statement true or false?Here we have the equation:
logₐ(x^3 + y^3) = 3logₐ(x) + 3logₐ(y)
And we want to see if it is true.
First, remember two rules:
logₐ(x^n) = n*logₐ(x)
and:
logₐ(x) + logₐ(y) = logₐ(x*y)
Then, the right side of the statement can be rewritten as:
3logₐ(x) + 3logₐ(y)
3(logₐ(x) + logₐ(y)) = 3*logₐ(x*y) = logₐ((x*y)^3)
And that is different to what we got in the statement, so the statement is false.
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Find the probability that a point chosen at random would lie in the shaded area of the figure. Round to the nearest tenth of a percent.
Answer:
Area of shaded region:
12r^2 - (2(2r^2) + 2πr^2) =
12r^2 - 4r^2 - 2πr^2 =
(2r^2)(4 - π)
Probability of point chosen in shaded region:
(2r^2)(4 - π)/(12r^2) = (4 - π)/6 = .143 = 14.3%
Jasmine sold 5 cherry pies and 12 Lemmon mer
Answer:
6
Step-by-step explanation:
this is if you meant: Jasmine sold 5 cherry pies and 12 lemonade how much more did Jasmine sell of lemonade than cherry pies
