To simplify the given product, we can use the properties of radicals. By assuming d ≥ 0 the product is [tex]3^{(3/2)} \times d^{(3/2)}.[/tex]
Specifically, the product of radicals with the same index can be expressed as a single radical by multiplying their radicands.
In this case, we have:
3√d × 3√d × 3√d
We can write this as a single radical by multiplying the radicands:
[tex]3 \sqrt{d} \times 3\sqrt{d} \times 3\sqrt{d} = (3 \sqrt{d})^3[/tex]
To evaluate this expression, we can use the property of exponents that states that the cube of a number is equal to that number raised to the third power.
Thus:
[tex](3 \sqrt{d})^3 = 3 \sqrt{d} \times 3\sqrt{d} \times 3 \sqrt{d}[/tex]
[tex]= 3^{(3/2)} \times d^{(3/2)}[/tex]
Therefore, the simplified product is [tex]3^{(3/2)} \times d^{(3/2)}.[/tex]
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someone please tell what to do with this i am lost
The properties used to simplify the expression are given as follows:
2. Combine like terms.4. Division property.How to simplify the expression?In algebra, the combination of like terms refers to the process of simplifying expressions by adding or subtracting terms that have the same variable(s) raised to the same power(s).
In this problem, from step 1 to step 2, on the left side of the equality, all the terms with the variable n and exponent 1 were added, as were the constant terms, hence the like terms were combined.
In Step 4, the variable n was obtained applying the division operation, which is the inverse operation of the multiplication operation in Step 3.
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Un vendedor de seguros recibe un salario semanal más una comisión, la cual es un porcentaje de sus ventas. En una semana, por ventas de $3 000 su pago fue de $850. En la siguiente semana por ventas de $4 000 su pago total fue de $1000. Determinen su salario semanal y el porcentaje de comisión.
Answer:
RESOLUCIÓN.
Para resolver este problema hay que seguir los siguientes pasos:
1) Determinar la comisión del vendedor de seguros.
Se sabe por datos del problema que cuando vendió $3000 su sueldo total fue de $850 y cuando vendió $4000 su sueldo total fue de $1000, eso quiere decir que:
Venta = 4000 - 3000 = $1000
Sueldo = 1000 - 850 = $150
Es decir que por cada $1000 en ventas, su ganancia es de $150.
1000 ---> 100%
150 ---> x
x = 150 * 100 / 1000 = 15%
Por lo tanto el porcentaje de comisión del vendedor es de 15% por venta.
2) Determinar el salario semanal fijo del vendedor.
Una vez conocido el porcentaje de comisión se puede obtener el salario fijo.
Para el primer caso:
850 = Salario fijo + Comisión
Comisión = 3000 * 15/ 100 = $450
Por lo tanto se tiene que:
850 = Salario fijo + 450
Salario fijo = $400
Por lo tanto se tiene que el salario semanal del vendedor es de $400.
Step-by-step explanation:
if 85% of 'a' is 'b' then which of the following is true a, a=b b,ab
Answer:
Step-by-step explanation:
The statement "85% of 'a' is 'b'" can be represented mathematically as:
0.85a = b
This means that 'b' is 85% of 'a'.
To answer the question:
a = b/0.85
So, a is equal to 'b' divided by 0.85.
Therefore, the correct option is (a) a=b.
A cone has a base area of 24 square inches and a height of 8 inches. What is the area of a cross-section of the cone that is parallel to the base and 3 inches from the vertex?
A circular cross section is marked near the vertex of a cone, parallel to the base.
The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is square inches.
The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is 27/8 square inches or 3 3/8 square inches
Calculating the area of the cross section of a coneFrom the question, we are to determine the area of the cross-section of the cone
To determine the area of the cross-section of the cone, we will determine the radius of the cross-section.
Let the radius of the cross-section be x and radius of the base of the be r.
The height of the cone is 8 inches and the height of the cone formed from the cross-section is 3 inches
By similar triangle theorem, we can write that
8/r = 3/x
x = (3r)/8
From the given information,
The area of the base is 24 square inches
Thus,
πr² = 24
Therefore, r² = 24/π
The area of the cross-section will be
A = πx²
But, x = (3r)/8
Thus,
A = π [(3r)/8]²
A = π × 3²/8² × r²
A = π × 9/64 × 24/π
A = 27/8 square inches
Hence, the area is 27/8 square inches or 3 3/8 square inches
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Find the linear function with the following properties.
f(0)=6
Slope of f=−9
Answer:
y = - 9x + 6
Step-by-step explanation:
the equation of a linear function in slope- intercept function is
y = mx + c ( m is the slope and c the y- intercept )
given slope = - 9 and f(0) = 6 , that is the point (0, 6 ) , then c = 6
y = - 9x + 6 ← linear function
Brett has pieces of steel that are 8 in. and 12 inch. Long he wants to weld the pieces together with a third piece of steel to make. Triangular frame what is the range of the lengths he can use for the third piece
The range of lengths Brett can use for the third piece of steel is 4 in. < x < 20 in.
What is triangle inequality theorem?The Triangle is a polygon with three line segments as its boundaries. That is the tiniest polygon imaginable. Three vertices, three internal angles, and three sides make up a triangle.
The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for every triangle, the sum of the lengths of the first two sides is always higher than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.
Using the triangle inequality theorem we have:
8 + 12 > x
x + 8 > 12
x + 12 > 8
20 > x
x > 4
x > -4
Therefore, the range of lengths Brett can use for the third piece of steel is 4 in. < x < 20 in.
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Gaby logra duplicar su dinero y pagar 70,000 que debía;le queda. 90,000 cuánto dinero tenía Gaby al inicio
Answer:
logra =70000
queda=90000
Step-by-step explanation:
additional
total income 70000+90000=160000
division by 2
160000/2
=$80.000
Determine the value of y, if x is - 2.
y = x + 8
answer: 10
y = |2| + 8
y = 2 + 8
y = 10
△ABC and △DEF are similar triangles. Find BC.
The length of side BC is solved to be 24 units
How to find BCThe problem gave that the two triangles are similar triangles and the proportions will be used to find the length of BC as below
5 / (x - 4) = (x + 7) / 12
cross multiplying
60 = (x - 4) (x + 7)
60 = x^2 + 3x - 28
x^2 + 3x - 88 = 0
x = 8 or -11
take the positive value hence x = 8
Solving for BD
side DE = x - 4 = 8 - 4 = 4
taking proportions we have
DE / FE = AB / BC
4 / 8 = 12 / BC
BC = 8 * 12 / 4 = 24
therefore length of BC is equal to 24 units
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Juan is hiking a trail that is 2 miles long. He hikes 14 miles before resting.
How much farther does he have to hike?
Answer:
I think the answer is D.) 7/8 mile
Step-by-step explanation:
If you make the mixed numbers improper fractions. 2 and 1/8 is 17/8, 1 and 1/4 (2/8) is 10/8, then you subtract the numerators and keep the denomitators the same to get 7/8 mile (sorry if I spelt something wrong)
can someone please help me on this one
? cubic cm
Volume, it is defined as the space occupied within the boundaries of any three-dimensional solid.
What is volume?Volume is defined as a capacity occupied or captured by a 3-dimensional solid shape. It is difficult to visualise in any shape, yet it may be compared amongst shapes. For instance, a geometry box has a larger or bigger volume than an eraser placed inside of it. We split the area into equal square units to determine or get the area of any 2-dimensional form.
Cuboid, is a 6-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid is short for "like a cube".
[tex]Volume\ of \ Cuboid = Length * Breadth * Height[/tex]
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Please help me solve these questions that are attached.
The sums, differences, product, and quotient of the functions and their domains are;
f(x) = √(16 - x^2), g(x) = √(x + 3)
f + g = √(16 - x^2) + √(x + 3)
Domain; [-3, 4]
f - g = √(16 - x^2) - √(x + 3)
Domain: [-3, 4]
f × g = √(16 - x^2) × √(x + 3) = √(-x³ - 3·x² + 16·x + 48)
f × g = √(-x³ - 3·x² + 16·x + 48)
Domain; [-3, 4]
f/g = √(16 - x^2)/√(x + 3) = √(16 - x^2)/(x + 3))
f/g = √(16 - x^2)/(x + 3))
Domai; [-3, 4] ∪ [1, 4]
f(x) = √(81 - x^q2), g(x) = √(x² - 16)
f + g = √(81 - x^2) + √(x² - 16)
Domain [-9, -4] ∪ [4, 9]
f - g = √(81 - x^2) - √(x² - 16)
Domain: [-9, -4] ∪ [4, 9]
f × g = √(81 - x^2) × √(x² - 16) = √(-x⁴ + 97·x² - 1296)
f × g = √(-x⁴ + 97·x² - 1296)
Domain: [-9, -4] ∪ [4, 9]
f/g = √(81 - x^2)/√(x² - 16)
Domain: [-9, -4] ∪ [4, 9]
What is the sum of two functions?The sum of two functions is obtained by adding the values of the functions at each point.
The sum of two functions is obtained by adding the values of the functions at each point. The domain of the sum is the intersection of the domains of the two functions, In this case, the domain of f + g is [-3, 4]
The difference of two functions is obtained by subtracting the functions values at each point. The domain of the difference is the intersection of the domains of the two functions. In this case, the domain of f - g is [-3, 4]
The product of two functions is obtained by multiplying the values of the functions at each point. The domain of the product of the functions is the domain of the intersection of the domains of the two functions. The domain of f × g is [-3, 4]
The quotient of two functions is obtained by dividing the values of the functions at each point. The domain of the quotient is the same as the domain of the intersection of two functions, excluding any points where the denominators is zero. The domain of f/g is [-3, -1] ∪ [1, 4].
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Please help!
What is the principal square root? And why is it used when solving radical
polynomials?
Answer:
The principal square root of a non-negative real number is the positive square root. For example, the principal square root of 25 is 5, since 5^2 = 25.
When solving radical polynomials, the principal square root is used because it is the most commonly used square root. In many contexts, including mathematical and scientific calculations, the principal square root is the default choice unless otherwise specified. Additionally, when working with radical expressions, we often simplify expressions by taking the principal square root, as it can help us to simplify calculations and express answers more clearly.
Tara uses 6.6 pints of white paint and blue paint to paint her bedroom walls. 3 4 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Answer:
1.65 pints
Step-by-step explanation:
If Tara used 6.6 pints of white and blue paint combined, and 3/4 of that amount is white paint, then we can find the amount of white paint she used by multiplying 6.6 by 3/4:
6.6 x 3/4 = 4.95
So Tara used 4.95 pints of white paint to paint her bedroom walls.
To find out how much blue paint she used, we can subtract the amount of white paint from the total amount of paint:
6.6 - 4.95 = 1.65
Therefore, Tara used 1.65 pints of blue paint to paint her bedroom walls.
A dice is tossed once,what is the probability that a prime number shows upwards
What is the length of line segment AC?
Using geometry, we can find that the length of the line segment AC as per the distance between two points is= 18 ft.
What are line segments?
In geometry, a line segment's borders are determined by two distinct points on the line. Any portion of a line that connects two places is referred to as a line segment.
A segment has an endpoint, whereas a line doesn't.
What are some examples of line segments in the real world?
a scale, a ruler, a stick, and a boundary line.
Thus, the length of the line segment AC is = 18ft.
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What is x-²y (x³y5)³ in simplest form for all values of x and y where the expression is defined?
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used
-18-12 4
X
7
8
9 15 16
Step-by-step explanation:
To simplify the expression x^-2y(x^3y^5)^3, we need to perform the operations inside the parentheses first, using the exponent rule that (a^m)^n = a^(mn):
x^-2y(x^3y^5)^3 = x^-2y(x^(33)y^(53)) = x^-2y(x^9y^15)
Next, we can simplify the expression by multiplying the coefficients (numbers) and adding the exponents of x and y, using the product rule that x^mx^n = x^(m+n) and (xy)^m = x^my^m:
x^-2y(x^9y^15) = (1y/x^2)(x^9*y^15) = y^(15+1)x^(9-2) = y^16x^7
Therefore, the simplified form of x^-2y(x^3y^5)^3 is y^16*x^7.
Note that this expression is defined for all values of x and y except for x=0.
Attendance for local baseball games has been increasing by an average of 10% per year for the last few years. In 2020, the average attendance was 100 people. Predict the average number of people attending local teseball games in 2024 if this trend continues. Round to the nearest whole number.
people
To predict the average number of people attending local baseball games in 2024, we need to use the formula:
A = P(1 + r)^n
where:
A = the predicted average attendance in 2024
P = the current average attendance (in 2020)
r = the annual growth rate (as a decimal)
n = the number of years of growth (from 2020 to 2024)
Given that the annual growth rate is 10% and the number of years of growth is 4 (from 2020 to 2024), we have:
r = 0.10
n = 4
Substituting these values and the current average attendance of 100 people into the formula, we get:
A = 100(1 + 0.10)^4
A = 100(1.10)^4
A = 100(1.4641)
A = 146.41
Therefore, the predicted average number of people attending local baseball games in 2024 is approximately 146 (rounded to the nearest whole number).
help quick!!! plsssss
Since an actual mosquito is about 1.6 cm, the scale factor of the diagram is equal to 2.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (actual figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image (actual figure)
Conversion:
1 cm = 10 mm
1.6 cm = 1.6 × 10 = 16 mm.
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = 32/16
Scale factor = 2.
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Together, teammates Pedro and Ricky got 2686 base hits last season. Pedro had 280 more hits than Ricky. How many hits did each player have?
Answer:
1483 pedro 1203 ricky
Step-by-step explanation:
1203+1483 = 2686
help me please bro please
The figure which could not be a cross section of a right circular cone is option a and d.
Describe Right Circular Cone?A right circular cone is a three-dimensional geometric shape that has a circular base and a vertex directly above the center of the base, such that the axis passing through the vertex and the center of the base is perpendicular to the base.
The base of the cone is a circle, and the sides of the cone slope upward to meet at the vertex. The distance from the vertex to the center of the base is called the height of the cone, denoted by h, and the distance from the center of the base to any point on the edge of the base is called the radius, denoted by r.
The lateral surface of the cone is curved, while the base and the vertex are flat. The angle formed between the height and the slant height (the distance from any point on the base to the vertex) is called the half vertical angle or the apex angle of the cone, denoted by θ.
The formula for the volume of a right circular cone is given by V = (1/3)πr²h, while the formula for the lateral surface area of a right circular cone is given by L = πrℓ, where ℓ is the slant height of the cone, which is equal to √(r² + h²).
Circle and eclipse cannot be cross section of a right circular cone.
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PLEASE ANSWER BEFORE 11:59 TONIGHT
1. A factory needs two raw materials. The probability of not having an adequate supply of material A is 0.05, whereas the probability of not having an adequate supply of material B is 0.03. A study determines that the probability of a shortage in both A and B is 0.01. a. Let E be the event "shortage of A" and F be the event "shortage of B". Construct a Venn diagram representing events E and F.
The Venn diagram needed based on the question is given below:
The Venn Diagram__________
/ \
/ A \
/____________\
\ /
\ E ∩ F /
\_________/
B
In the diagram, the set A represents the event of having an adequate supply of material A, and the set B represents the event of having an adequate supply of material B.
The overlap of A and B represents the event of having an adequate supply of both materials.
The set E represents the event of a shortage in material A, and the set F represents the event of a shortage in material B.
The intersection of E and F, denoted by E ∩ F, represents the event of a shortage in both materials.
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what is the correct answer
Answer:
54 square meters
Step-by-step explanation:
Given the scale is 1 centimeter represents 3 meters, to scale the dimensions of the drawing to the dimensions of the actual room, multiply the dimensions of the drawing by 3.
Therefore:
3 cm × 3 = 9 m2 cm × 3 = 6 mSo the dimensions of the actual room are:
Length = 9 mWidth = 6 mThe area of a rectangle is the product of its width and length.
Therefore, the area of the actual room is:
Area = 6 × 9 = 54 m²Can you help me find this answer
Answer:
4
Choice D
Step-by-step explanation:
[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\dfrac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}[/tex]
[tex]\mathrm{Periodicity\:of\:}\cos \left(x\right)\:\mathrm{is}\:2\pi[/tex]
How would you characterize the relationship between the hours spent on homework and the test
scores? Explain.
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h
of homework?
(c) What does the number 40 in Part (b) mean in the context of the situation
Paul scοre 64 fοr the mοdel predict fοr 3 h οf hοmewοrk and test scοre tο be 40.
What is function?A functiοn is defined as a relatiοnship between a set οf inputs that each have οne οutput. A functiοn is a relatiοnship between inputs in which each input is related tο exactly οne οutput. Every functiοn has a dοmain and a cοdοmain, as well as a range. In general, a functiοn is denοted by f(x), where x is the input. A functiοn's general representatiοn is y = f. (x).
Scοre can be defined as tοtal number which any persοn achieve after dοing any wοrk οr target. Suppοse a Batsman make 100 run it means he scοre 100 fοr his team.
a. Fοr three hοurs οf study we have that the nοte wοuld be apprοximately:
y = 8x + 4
b. The number 40 means that if yοu dο nοt devοte any study time, then yοu expect the test scοre tο be 40.
y = 8(3) + 40
y = 64
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I will mark you brainiest!
In a proof to show two triangles are congruent if a given is PR ⟂ CK, which of the following statements most likely will be used within the proof?
A) PR and CK are congruent.
B) PR and CK are similar.
C) PR and CK form acute angles.
D) PR and CK form right angles.
Answer:
D) PR and CK form right angles
Step-by-step explanation:
⟂ is the symbol for a perpendicular, so it is a perpendicular bisector.
- Perpendicular bisectors divide an angle into 2 90° angles.
If 25% of a number is 10, find 5% of that number.
Answer:
0.125
Step-by-step explanation:
Answer:
5% of 40 is 2
Step-by-step explanation:
number = x
25% of x is = 10
25% = 25/100, or 1/4
[tex]\frac{1}{4}x = 10[/tex]
multiply each side by 4
[tex]x = 40[/tex]
5% is 5/100, or 1/20
[tex]\frac{1}{20}x = ?[/tex]
plug-in the known value
[tex]\frac{1}{20}*40 = ?\\\frac{40}{20} = ?\\\frac{4}{2} = ?\\\\? = 2[/tex]
What is a frequency distribution?
Answer:
Frequency distributions are visual displays that organize and present frequency counts so that the information can be interpreted more easily.
Step-by-step explanation:
The distribution of a variable is the pattern of frequencies, meaning the set of all possible values and the frequencies associated with these values.
Solve 58 - 10x ≤ 20 + 9x.
Need help Mav has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $425.05.
She buys 4 bicycle reflectors for $15.19 each and a pair of bike gloves for $15.79.
She plans to spend some or all of the money she has left to buy new biking outfits for $29.20 each.
Write and solve an inequality which can be used to determine
o, the number of outfits Mav can purchase while staying within her budget.
The inequality x ≤ 3 indicates how many different bicycle outfits she can purchase.
How do you write inequality and solve it?She has $560 to spend at a bike shop on new accessories and clothing for riding.
For $425.05. she spends on a brand-new bicycle.
She spends $15.19 for each of four bicycle reflectors and $15.79 on a pair of cycling gloves.
She intends to use all or part of the remaining funds to purchase new bicycle clothing at $29.20 each.
The disparity that can be used to calculate how many garments she can purchase for her budget is as follows:
let
x = the number of garments
Therefore,
425.05 + 15.19(4) + 15.79 + 29.20x ≤ 560
425.05 + 60.76 + 15.79 + 29.20x ≤ 560
29.20x ≤ 560 - 425.05 - 60.76 - 15.79
29.20x ≤ 58.4
Divide the difference between the two sides by 29.20.
x ≤ 58.4 / 19.20
x ≤ 3.04166666667
x ≤ 3
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The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 119 and standard deviation of 18 .
Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.
a. Around what percentage of adults in the USA have stage 2 high blood pressure? Give your answer rounded to two decimal places.
%
b. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the nearest person. Note: I had a bit of an issue encoding rounded answers, so try rounding both up and down if there's an issue!
a) The percentage of adults in the USA that have stage 2 high blood pressure is; 0.27%
b) The number of people that you will expect to have BP greater than 160 is; 54
How to get p-value from z-score?a) if x is systolic blood pressure, then want to find probability that x ≥ 160.
The formula for z-score is;
z = (x - mean)/standard deviation
Thus;
z = (x - 119)/18
This is normally distributed with mean 0 and standard deviation 1
Transform x to z:
P(x > 160) = P(z > (160 - 119)/18)
= P(z > 2.78)
= P(z < -2.78)
= 0.0027 (from standard normal distribution table, which 0.27%.)
b) Since probability of BP > 160 is 0.027.
Then out of 2000 people, then 2000 * 0.027 = 54 people would have BP > 160.
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