Answer:
g = 9
Step-by-step explanation:
9√g + 58 = 85
9√g = 85 - 58
9√g = 27
√g = 27/9
√g = 3
g = 3²
g = 9
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
What is the equation of the line in slope intercept form using these points?
Answer:
y = -x - 1
Step-by-step explanation:
1. The slope-intercept form of any linear equation is y = mx + b, where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept.
2. To find the slope given two points, we can use the formula \(\frac{y_2-y_1}{x_2-x_1}\) and plug in the corresponding variable.
\(\frac{5-(-2)}{-6-1}\) \(\frac{5+2}{-7}\) \(\frac{7}{-7}\) \(-1\)3. Okay, so the slope is -1x or just -x. This means that the equation looks like this so far: y = -x + b
4. To find b, the y-intercept, we can take the equation of \(b = y_1 - m * x_1\) and plug in the values!
\(b = -2-(-1)*1\) \(b = -2 + 1 * 1\)\(b = -1 * 1\) \(b = -1\)5. Now that we have our y-intercept and slope, let's plug in those values and find the equation!
\(y = -x - 1\)Therefore, the equation of the line is y = -x - 1. I hope this helped you!
27 As shown in the diagram below, secants PWR and PTS are drawn to circle O from external point P.
12/
O.
W
T
P5
If m/RPS = 35°and mRS = 121°, determine and state mWT.
By applying the Theorem of Intersecting Secant, the measure of angle WT is equal to 51°.
How to determine angle m<WT?By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the Theorem of Intersecting Secants.
What is the Theorem of Intersecting Secants?The Theorem of Intersecting Secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the Theorem of Intersecting Secant, angle P will be given by this formula:
m<P = ½ × (m<RS - m<WT)
Substituting the given parameters into the formula, we have;
35 = ½ × (121 - m<WT)
70 = 121 - m<WT
m<WT = 121 - 70
m<WT = 51°.
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Put the following equation of a line into slope-intercept form, simplifying all fractions. 3y-9x=-6
Answer: y=3x-2
Step-by-step explanation:
3y-9x=-6
First you will need to add 9x to the other side so your equation will look like 3y=9x-6. Then you need to divide all the numbers by 3. So 3y divided by 3 and 9 divided by 3 and -6 divided by 3. Your final answer should be y=3x-2.
Answer:
This equation in slope intercept form would be y = 3x - 2
Step-by-step explanation:
The following is how to solve this equation:
3y - 9x = -6
+9x +9x
----------------------
3y = 9x - 6
divide each of the numbers by 3
So the answer is y = 3x - 2
I really think it’s B ...Help?
find the area and circumference of a circle with a radius 5 m. use the value 3.14 for radius, and do not round your answers. Be sure to include the correct units in your answers.
Area and circumference of the circle are 78.5 m² and 31.4 m respectively.
What is a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that, a circle have a radius 5 m
Area of a circle = π × radius²
Circumference = 2π×radius
Area = 3.14 × 5² = 3.14 × 25 = 78.5 m²
Circumference = 3,14 × 2 × 5 = 31.4 m
Hence, area and circumference of the circle are 78.5 m² and 31.4 m respectively.
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Need this ASAP thanks
Answer:
the answer is A substitution
A Bakery allows customers to design and order special cupcakes. There is a single fee of $4 to create the new design and then each special cupcake ordered costs $3.
thy be c matey truth me ARG!!??
Answer:7$
Step-by-step explanation:$4+3$=7$
write the equation in standard form: 4x - 3 = 5y
Answer:
4x−5y=3
Step-by-step explanation:
Answer:
Step-by-step explanation:
Solve for x when sin(4x)=1/2
the most simple answere please
Answer:
x=7.5
Step-by-step explanation:
To cancel out the sin function we need to mulitplly it by sin⁻¹ (you can usually access this button if you press 2nd-->sin)
so sin⁻¹(.5)=30
30=4x
x=7.5
What is the approximate area of the shaded sector in the circle shown below
Answer:
51.3
Step-by-step explanation:
The formula is Θ/360 × πr²
30/360 × 22/7 × 14²
30/360 × 22/7 × 196
= 51.3
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the:___________.
A. width of the confidence interval to increase.
B. width of the confidence interval to decrease.
C. width of the confidence interval to remain the same.
D. sample size to increase.
Answer: A. width of the confidence interval to increase.
Step-by-step explanation:
A 95% confidence interval provides a interval with a 95% probability that the true population parameter lies in it , where 99% confidence interval provides a interval with a 99% probability that the true population parameter lies in it .
Probability of getting true population parameter increases if the width of the interval increases.
Hence, if we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the width of the confidence interval to increases.
hence, the correct option is A.
5. (03.01 MC)
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. (1 point)
Using this property on the given expression, we get:
\({(x^3/4)^2/3} = x^(3/4*2/3)\) {multiplying the exponents}= \(x^(1/2)\)
Now, we can rewrite the expression in radical form as √x which is the required answer.
The given expression to rewrite with rational exponents as a radical expression by extending the properties of integer exponents is:
\({(x^3/4)^2/3}\)
To rewrite this expression with rational exponents as a radical expression by extending the properties of integer exponents, the general formula of the power rule of exponents can be used, which states that \((a^m)^n = a^(mn)\).
Now applying this power rule of exponents on the given expression:
\({(x^3/4)^2/3}={x^(3/4*2/3)}={x^(1/2)}\)= √x
Hence, the required expression, when rewritten with rational exponents as a radical expression by extending the properties of integer exponents, is √x.
To understand the solution, let's understand the concepts and formulas used in it.
The given expression is {(x^3/4)^2/3}. Now, to rewrite this expression with rational exponents as a radical expression by extending the properties of integer exponents, we need to use the power rule of exponents.
The power rule of exponents is an important property of the exponents that states that when we raise a power to another power, we need to multiply the exponents.
That is (a^m)^n = a^(mn).
Using this property on the given expression, we get:
\({(x^3/4)^2/3} = x^(3/4*2/3)\) {multiplying the exponents}= \(x^(1/2)\)
Now, we can rewrite the expression in radical form as √x which is the required answer. Hence, the given expression rewritten with rational exponents as a radical expression by extending the properties of integer exponents is √x.
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help please. And can I have the explanation so I can understand better, thank you!!
x²-11x+28 please answer
(URGENT)!!!!!!!
Write one sentence that addresses the issue of globalization from the text and one sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers
Answer:
Step-by-step explanation:
One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.
One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence
How long it will take 2000$ to double if it is invested at 6% interest compounded semi annually
Answer:
Number of year = 11.725 year (Approx.)
Step-by-step explanation:
Given:
Amount invested = $200
Interest rate = 6% (compounded semi annually)
Future value = 2 x Amount invested
Find:
Number of year
Commutation:
Future value = 2 x Amount invested
Future value = 2 x 200
Future value = $400
Number of year (Semi-annual) = 2n
Interest rate (Semi-annual) = 6% / 2 = 3%
So.
A = P[1+r]ⁿ
400 = 200[1+3%]²ⁿ
2 = [1.03]²ⁿ
n = 11.725 year
Number of year = 11.725 year (Approx.)
(4x² - 7xy)(1/8x² - 2/7xy) find the product
Answer:
first of all you have to introduce the expansion of the terms giventherefore solve;
4x²(1/8x²-2/7xy) - 7xy(1/8x²-2/7xy)
we get;
½x⁴- 8/7x³y - 7/8x³y + x²y²
½x⁴-113/56x³y + x²y²
Select the true statement.
Answer: D) 54 inches = 1 1/2 yards
explanation: 1 1/2 yards = 54 inches.
Solve the equation.
∣x−2∣=∣4+x∣
Ax + By=C
solve for x
The Chess Club president brought donuts to the club meeting each week. As the club grew, more donuts were needed so that each member could have a donut. The table below shows the ratios of boxed donuts to the cost.
Donuts A 4 5 C
Cost 13.80 27.60 B 55.20
Determine which table has the correct values for A, B, and C.
Donuts 3 4 5 7
Cost 13.80 27.60 34.95 55.20
Donuts 2 4 5 8
Cost 13.80 27.60 34.95 55.20
Donuts 3 4 5 6
Cost 13.80 27.60 34.50 55.20
Donuts 2 4 5 8
Cost 13.80 27.60 34.50 55.20
The table with correct values of A, B and C is,
⇒ Donuts 2 4 5 8
Cost 13.80 27.60 34.50 55.20
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
We have to given that;
The table below shows the ratios of boxed donuts to the cost.
Donuts A 4 5 C
Cost 13.80 27.60 B 55.20
Now, By definition of ratio, we get;
⇒ A / 13.80 = 4 / 27.60
⇒ A = 13.80 × 4 / 27.60
⇒ A = 2.00
And,
⇒ 4 / 27.60 = 5 / B
⇒ B = 5 × 27.60 / 4
⇒ B = 34.5
⇒ 4 / 27.60 = C / 55.20
⇒ C = 55.20 × 4 / 27.60
⇒ C = 8
Thus, The table with correct values of A, B and C is,
⇒ Donuts 2 4 5 8
Cost 13.80 27.60 34.50 55.20
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Answer:
a
Step-by-step explanation:
i took the test :)
Simplify the following expression. 7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}
The term, \(\frac{1}{49}\) is simplified form of the expression \(7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}\).
What is simplest form?The top and bottom of a fraction are said to be in its simplest form if they only share the number one. For the top & bottom to remain whole numbers, you cannot divide them further.
Additionally, lowest terms, or simple form, may be used.
The simplest form of a fraction, for instance, is 4/5. Apart from 1, there isn't a number that divides both 4 and 5. Not in its simplest form is the fraction 3/6. Numerator & denominator can both be divided by 3.
Given to simplify the expression
\(7^{-\dfrac{5}{6}} \ \cdot\ 7^{-\dfrac{7}{6}}\)
\(7^{(-\dfrac{5}{6}-\dfrac{7}{6})}\)
\(7^{(\dfrac{-5-7}{6})}\)
\(7^{(\dfrac{-12}{6})}\)
\(7^{(-2)}\)
\(\dfrac{1}{7} \times \dfrac{1}{7}\)
\(\dfrac{1}{49}\)
Thus, \(\frac{1}{49}\) is simplified form of the expression \(7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}\).
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What is the shape of the cross section of a sliced cylinder
A sliced cylinder's cross section can be any shape that can be formed by intersecting a cylinder with a plane.
How to determine the shape?The shape of a sliced cylinder's cross section is determined by the angle and position of the slice.
If the slice is made parallel to the cylinder's base, the cross section is a circle.
If the slice is made at an angle to the cylinder's base, the cross section is an ellipse.
If the slice is made perpendicular to the cylinder's base, the cross section is a rectangle.
In general, a sliced cylinder's cross section can be any shape formed by intersecting a cylinder with a plane.
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How do we know where to label base and where to label height on a trapezium. does it matter where they are on the trapezium or does it have to be in rectangular please help on question
The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.
In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.
Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.
Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.
It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.
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Julian’s friend James also has a tank in the shape of a triangular prism. The dimensions of James’ tank are each exactly 2 3/4 times the dimensions of Julian’s tank. If the area of the triangular base of Julian’s tank is approximately 400 square inches, what is the approximate area of the triangular base of James’ tank?
3,025 square inches
2,035 square inches
3,045 square inches
4,025 square inches
The approximate area of the triangular base of James’ tank is 3025 in²
To find the approximate area of the triangular base of James' tank, we need to know what scale is.
What is scale?A scale is the ratio of two dimension. It is given by scale = New dimension/old dimension
Given that the dimensions of James’ tank are each exactly 2 3/4 times the dimensions of Julian’s tank.
The scale of the area of James' tank to the area of triangular base of Julian's tank is S = (2³/₄)²
= (11/4)²
= 121/16
Let
A = area of triangular base of James' tank, A' = area of triangular base of Julian's tank = 400 in²So, scale, S = A/A'
The approximate area of the triangular base of James’ tankSo, making A subject of the formula, we have
A = SA'
A = 121/16 × 400 in²
A = 121 × 25 in²
A = 3025 in²
So, the approximate area of the triangular base of James’ tank is 3025 in²
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Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Since corresponding parts of
congruent triangles are congruent, angle ZWY is congruent to angle XWY and angle ZYW is congruent to angle XYW.
True or False: Mai can now conclude that diagonal WY bisects angles ZWX and ZYX.
True
O False
It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX
Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:
Diagonal WY bisects angles ZWX and ZYX because:
all corresponding parts of both triangles are congruent. (Option A).
If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.
Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.
If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).
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is this graph a minimum or a maximum pls help
The vertex of the graph is a maximum at (-2, 4)
Calculating if the vertex of the graph a maximum or a minimum?From the question, we have the following parameters that can be used in our computation:
The graph
The graph is a quadratic function
From the graph, we can see that the graph has a maximum value
This maximum value represents the vertex of the graph
And it is located at (-2, 4)
So, we have
Maximum = (-2, 4)
Hence, the maximum value of the function is (-2, 4)
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In each blank below a single digit is inserted such that the following six three-digit numbers, in this order, form an arithmetic sequence: 1_ _, _ _ 9, 2 _ 2, _ 6 _, 2 _ _, _ 3 _What is the value of the next number in the sequence?
The series appears to be 166, 199, 232, 265, 298, 331
With examples, define sequence?
A list of numbers in a certain order is known as a sequence. A term is the name given to each number in a sequence.
In a series, each term has a place (first, second, third and so on). Take the sequence 5, 15, 25, 35, as an example. Each number is referred to as a word in the sequence.
The last number of the common difference must end in 3
And this must be a 2 digit number
So....the first number must end in 6
The the 4th number must be 265
So..... the 5th number must end in 8
And the last digit of the last term must end in 1 [ and begin with 3 ]
Putting all this together we have that
265 + 2d = 331
2d = 66 ⇒ d = 33
So the first term must be 265 - 3 (66) = 166
the series appears to be 166, 199, 232, 265, 298, 331
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Cushing, Inc., costs products using a normal costing system. The following data are available for last year:
Budgeted:
Overhead $357,000
Machine hours 140,000
Direct labor hours 17,000
Actual:
Overhead $355,000
Machine hours 137,000
Direct labor hours 16,500
Prime cost $753,500
Number of units 250,000
Overhead is applied on the basis of direct labor hours.
What was last year's per unit product cost?
a.$4.43
b.$3.01
c.$1.39
d.$4.40
Based on the predetermined overhead rate, last year's per unit product cost was d.$4.40.
What is the predetermined overhead rate?The predetermined overhead rate is the unit cost of overhead allocated to production units based on a cost driver, e.g., direct labor hours.
The overhead applied to the production units is computed by multiplying the predetermined overhead rate and the production units.
Budgeted:Overhead = $357,000
Machine hours 140,000
Direct labor hours 17,000
Predetermined overhead rate = $21 ($357,000/17,000)
Actual:Overhead = $355,000
Machine hours 137,000
Direct labor hours 16,500
Applied overhead = $346,500 ($21 x 16,500)
Prime cost $753,500
Total production costs = $1,100,000
Number of units 250,000
Unit cost = $4.40 ($1,100,000/250,000)
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