The correct option is option (d) 8 hours.
Amelia need to work for 8 hours to buy new sweater $40.
What is an equation and its solution?When two expressions are connected with the equals sign (=) in a math equation, it expresses the equality of the two expressions. A number that may be entered for the variable to produce a true number statement is the solution to an equation.
Let the hours Amelia need to work=h
Amalia paid=$20
Payment of each hour=$2.50
So, we can make an equation with given problem
40=20+2.50h
40-20=2.5h
20=2.5h
[tex]h=\frac{20}{2.5}[/tex]
h= 8
So, Amelia need to work for 8 hours to get $40.
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Pls answer question 8
Step-by-step explanation:
step 1: multiply [tex]2^m[/tex] by [tex]3^n[/tex]
2 × 3 = 6
to times power you must add them
eg: [tex]x^3[/tex] × [tex]x^4[/tex]3+4=7=[tex]x^7[/tex][tex]2^m[/tex] × [tex]3^n[/tex] = [tex]6^{m+n}[/tex]
step 2: rearrange
[tex]6^{m+n}[/tex] = 108
can you do this step by yourself
Which values represent solutions to cosine (startfraction pi over 4 endfraction minus x) = startfraction startroot 2 endroot over 2 endfraction sine x, where x is an element of [0, 2pi)?
The given trigonometric function consists of trigonometric values of common angles.
The values that represent the solution to [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex], x ∈ [0, 2·π) are; [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
What are trigonometric functions?Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.The given function is: [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex]
Where; x ∈ [0, 2·π).
We have; cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B).
[tex]cos(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}, sin(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}[/tex]Which gives:
[tex]cos(\frac{\pi }{4}-x )=\frac{\sqrt{2} }{2}. cosx+\frac{\sqrt{2} }{2}.sinx[/tex]So, we obtain:
[tex]\frac{\sqrt{2} }{2} .cosx=\frac{\sqrt{2} }{2}.sinx-\frac{\sqrt{2} }{2} .sinx=0\\cosx=0\\cos\frac{\pi }{2} =0[/tex]
Therefore, the possible solutions (x-values) to cos x = 0 are:
[tex]0[/tex] ≤ [tex]\frac{n.\pi }{2}[/tex] ≤ [tex]2.\pi[/tex]
Where, n = 1, 3, 5, .., x ∈ [0, 2·π)
We get: [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].
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400
300
200
100
2
4
6
8
X
Is the graphed function linear?
Yes, because each input value corresponds to
exactly one output value.
O Yes, because the outputs increase as the inputs
increase.
O No, because the graph is not continuous.
O No, because the curve indicates that the rate of
change is not constant.
It exists not linear the curve indicates that the rate of change exists not constant.
What is a linear Function?
Linear functions exist as those whose graph exists as a straight line. A linear function exists that can be characterized by the equation
y = mx + c, Where m exists the slope and c exists the intercept on the
y-axis. A linear function contains one independent variable and one dependent variable.
Therefore, the correct answer is option c) No, because the curve indicates that the rate of change is not constant.
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Use a left-hand sum with 4
intervals to approximate the area
under f(x) = 4 - x² between
x = 0 and x = 2.
Answer:
25 / 4
Step-by-step explanation:
To find the left sum, you need to....
1.) Find Δx
2.) Find [tex]x_{k-1}[/tex]
3.) Find ∑[tex]^n_{k=1}f(x_{k-1})[/tex]Δx
4.) Solve for the left sum
If you are playing a game that has a pair of dice you have to roll, what is the
probability that the sum of the numbers you roll will be a 9?
Probabilities are stated as fractions. For instance, the probability that you will get
heads on a coin flip are "1 out of 2" or 1/2. State your answer as a fraction in
simplest form.
Answer:
1/9
Step-by-step explanation:
For each of the first die's 6 outcomes, the second die also has a possible 6 outcomes.
6 × 6 = 36
There are 36 different outcomes from
1, 1
1, 2
1, 3
...
6, 6
Many outcomes have the same sum. For example, 3, 4 and 4, 3 both add to 7.
How many outcomes add to 9?
3, 6
4, 5
5, 4
6, 3
4 different outcomes out of a possible 36 different outcomes add to 9.
p(sum of 9) = 4/36 = 1/9
The graph below shows the results of a survey of vacations. Which explanation below can be used to explain the point (1,1400)?
The option that explains the point (1, 1400) is (c) the person surveyed took a day trip
How to explain the point (1,1400)?From the graph, we have the following representations:
x ⇒ number of days on vacationy ⇒ total cost of vacationThe point (1,1400) implies that
x = 1 and y = 1400
This means that
The number of days on vacation is 1 and the total cost of vacation is 1400
Hence, the option that explains the point (1, 1400) is (c) the person surveyed took a day trip
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. [Equations]
1/6x =4
Answer:
youre answer is here I hope it's right
x=24
Which table represents a function?
Answer:
choice d
Step-by-step explanation:
I hand this question
The cross-sectional areas of a triangular prism and a right cylinder are congruent. the triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. which conclusion can be made from the given information?
The conclusion can be made from the given information
The volume of the triangular prism is equal to the volume of the cylinder
Given that there are two figures
1. A right triangular prism
2. Right cylinder
The area of the cross-section of the prism is equal to the Area of a cross-section of the cylinder.
Let this value be A.
Also given that the Height of prism = Height of cylinder = 6
The volume of a prism is will be :
[tex]V _{prism} = cross section area \times height[/tex]
[tex]V _{prism} = A \times 6 = 6A[/tex] (1)
The Cross section of the cylinder is a circle.
hence the Area of the circle will be:
Area of cross-section, A = [tex]\pi \times r^2[/tex]
so, the Volume of the cylinder will be :
[tex]V _{cylinder} = \pi \times r^2 \times h[/tex]
[tex]V _{cylinder} = A \times h = A \times 6 = 6A[/tex] (2)
From equations (1) and (2) we can say that
The volume of the triangular prism is equal to the volume of the cylinder.
What is a triangular prism?A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry.If the sides of a right triangular prism are not rectangular, the prism is oblique. Right triangle prisms with square sides and equilateral bases are known as uniform triangle prisms.It is, in essence, a polyhedron with two parallel sides and three surface normals that are all in the same plane (which is not necessarily parallel to the base planes).There are parallelograms in these three faces. The identical triangle appears in every cross-section running parallel to the base faces.To learn more about triangular prism with the given link
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The half life of a substance is defined as the time required for the substance to decrease by half. If the weight of a substance begins at 128 grams, and the half life is 7 years, what will be the weight of the substance after 28 years?
the weight of the substance after 28 years is 8 grams.
How to determine the amountWe have that the half life of a substance is defined as the time required for the substance to decrease by half
The formula for calculating the half - life of a material is given as;
[tex]N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }[/tex]
Where
N(t) is final amountNo is the initial amount = 128 gramst1/2 is the half life = 7 yearst is the time elapsed = 28 yearsSubstitute into the formula
N(t) = 128 × (0. 5) ^28/ 7
N (t) = 128 × ( 0. 5) ^ 4
N(t) = 128 × 0. 0625
N(t) = 8 grams
Thus, the weight of the substance after 28 years is 8 grams.
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Q2. A train travels at a constant speed of 45 m/s. a) Calculate the distance travelled by the train in:
i) 30 s
ii) 2 minutes.
the train travels at 45 meters per each second
this question can be rewritten into the equation d = 45t, where d represents the distance traveled and t represents the time elapsed.
we are given two seperate times, so we can replace the variable t with each respective time. this leaves us with only one missing variable, so we can successfully isolate to find the other.
for i), we substitute t for 30 seconds, shown as follows
d = 45t
d = 45(30)
d = 1350m
for ii), we know that there are 60 seconds in every minute, so in multiplying 60 seconds by two we get the total amount of seconds in two minutes, which is 120.
we can now use 120 to substitute t in our equation
d = 45t
d = 45(120)
d = 5400m
hope this helps!!
Answer:
i) 1350 m
ii) 5400 m
Step-by-step explanation:
To calculate the distance traveled by the train, we can use the formula:
[tex]\large\boxed{\sf Distance=Speed \times Time}[/tex]
[tex]\hrulefill[/tex]
Question (i)Given values:
Speed = 45 m/s (meters per second)Time = 30 secondsSubstitute the given values into the formula for distance:
[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 30\;s\\& = \sf 1350\:m\end{aligned}[/tex]
Therefore, the train travelled a distance of 1350 meters in 30 seconds.
[tex]\hrulefill[/tex]
Question (ii)Given values:
Speed = 45 m/s (meters per second)Time = 2 minutesAs the time is given in a different unit of time than the speed, we must first convert the time into seconds. As 1 minute = 60 seconds, then:
[tex]\sf 2\; minutes = 60 \;s \times 2 = 120 \;s[/tex]
Substitute the given values into the formula for distance:
[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 120\;s\\& = \sf 5400\:m\end{aligned}[/tex]
Therefore, the train travelled a distance of 5400 meters in 2 minutes.
Please helppppp!!
Question #1 (Question un ) : What is the smallest positive integer k such that k/660 can be expressed as a terminating decimal?
Give BRAINLIST IF ANSWER!!!!!
Answer:
k = 33
Step-by-step explanation:
Terminating decimal numbers: Decimals that have a finite number of decimal places.
For a decimal to be terminating, the factors of the denominator must only contain 2 and/or 5. As 2 and 5 are prime numbers, use prime factorization to rewrite the denominator.
Prime factorization of 660:
⇒ 660 = 2 × 2 × 3 × 5 × 11
⇒ 660 = 2² × 3 × 5 × 11
Therefore:
[tex]\implies \sf \dfrac{k}{660}=\dfrac{k}{2^2 \cdot 3 \cdot 5 \cdot 11}[/tex]
The fraction will only be a terminating decimal if both 3 and 11 in the denominator are canceled out. To do this, their lowest common multiple must be the numerator:
⇒ LCM of 3 and 11 = 3 × 11 = 33
[tex]\implies \sf \dfrac{33}{660}[/tex]
[tex]\implies \sf k=33[/tex]
Therefore, the smallest positive integer k such that k/660 can be expressed as a terminating decimal is 33.
Answer:
33
Step-by-step explanation:
If the probability of a new employee in a fast-food chain still being with the company at the end of the year is 0. 5, what is the probability that out of 8 newly hired people?
The probability that out of 8 newly hired people is 3.2.
According to the statement
we have given that the some conditions and based on these conditions we have to find the probability that out of 8 newly hired people.
So, For this purpose,
we have given that the
new employee in a fast-food chain still being with the company at the end of the year is 0.5
Now, we See that is probability of remaining with the company.
There is only one is 0.5.
According to the probability law
P + Q = 1
and this become
Q = 1 - 0.60.
And the probability of one people hired is Q.
Then
Q = 0.4
And probability that out of 8 newly hired people is
8Q = 0.4 * 8
it become 3.2.
So, The probability that out of 8 newly hired people is 3.2.
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Lines de and ab intersect at point c. lines d e and a b intersect at point c. angle a c e is (2 x 2) degrees. angle e c b is (5 x 3) degrees. what is the value of x? 12 25 38 52
The correct option is B.
The value will be = 25
What is the Angles of the triangle?
The sum of the two interior angles that are not adjacent to it equals the exterior angles of a triangle, but the interior angles of a triangle always add up to 180°. Subtracting the angle of the desired vertex from 180° is another method for determining a triangle's exterior angle.
Suppose point C is where lines DE and AB converge.∠ACE = (2x+2)°
∠ECB = (5x+ 3)°
Angles ACE and ECB are additional angles according to the linear postulate, as seen in the attached diagram.
Therefore:
∠ACE+∠ECB = 180°
(2x+2)+(5x+3) = 180
2x+ 5x+ 2+ 3 = 180
7x + 5 = 180
7x = 175
x= 175/7
x = 25
Thus the value will be = 25
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I understand that the question you are lookin for is :
Lines de and ab intersect at point c. lines d e and a b intersect at point c. angle a c e is (2 x 2) degrees. angle e c b is (5 x 3) degrees. what is the value of x?
A.12
B. 25
C. 38
D. 52
Which situation will likely have no correlation?
B. number of dogs owned versus number of plane tickets bought
A six-sided die is rolled. What is the probability of rolling a four or an odd number?
Answer:
2/3 or 66%
Step-by-step explanation:
there are 3 odd numbers on a 6 sided die
3 + 1 = 4
4/6 = 2/3
The ratio of height to the base radius of a cone is 3:4. If the volume of the cone is 2000πcm³, find its radium, in cm.
Who can help me to answer this question? Please and thank you very much .
Answer:
20 cm
Step-by-step explanation:
The volume, V, of a cone with radius r and height h is given by the formula
V = [tex](1/3) \pi r^2 h[/tex]
Since it is given that the ratio of h to r is 3/4 we have the relationship
h/r = 3/4 ==> h = (3/4)r
Substituting for h in the volume equation gives us an expression in terms of r
[tex](1/3)\pir^2h = (1/3) \pi r^2 (3/4)r\\(1/3 ) (3/4) = 1/4\\[/tex]
So the expression simplifies to[tex](1/4)\pi r^3[/tex]
We are given that this volume is 2000π cm³
So
(1/4)πr³ = 2000π
Eliminating π on both sides and multiplying by 4 on both sides gives
r³ = 8000
r = ∛8000 = 20 cm Answer
Which expression is equivalent to x^2 + 5x - 6? Explain how.
(1) (x + 3) (x - 2)
(2) (x + 2) (x - 3)
(3) (x - 6) (x + 1)
(4) (x + 6) (x - 1)
Answer:
(4) (x + 6)(x - 1)
Step-by-step explanation:
Hello!Given expression
[tex]x { }^{2} + 5x - 6[/tex]
Find numbers when they are multiplied gives 6 and when they are added which gives 5.
Thus, these numbers are -1 & 6.
[tex]x {}^{2} + 6x - x - 6 \\ x(x + 6) - 1(x + 6) \\ (x + 6) \: \: (x -1 )[/tex]
Can also check the multiplied values of these two values.
Hope it helps!
Answer:
(4)
Step-by-step explanation:
Determine two multiples which when multiplied gives - 6(the last term in the equation), when added, gives +5 (the middle term in the equation).
Multiples are: +6 and -1
input the two multiples in place of the middle term (+5x)
=x^2+6x-1x-6
Collect like terms
=x(x+6)-1((x+6)
Answer= (x+6)(x-1)
Confirm answer above:
Open bracket
x(x-1)+6(x-1)
x^2-x+6x-6
x^2+5x-6 (initial equation).
Find x. A. 11√6/2 B. 22 C. 33 D. 11√3/2
Answer:
B
Step-by-step explanation:
using the tangent ratio on the triangle on the right and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then letting the altitude be h
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{11\sqrt{6} }{h}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by h )
11[tex]\sqrt{6}[/tex] = h × [tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
11[tex]\sqrt{2}[/tex] = h
using the sine ratio in the triangle on the left and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{x}[/tex] = [tex]\frac{11\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{2}[/tex] × x = 22[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
x = 22
I need this question to be done please I beg u.
It’s very important
I will fail if not done please help me
U must Determine the zeros of each following
Answer:
here's your answer step by step explanation
Step-by-step explanation:
page 6 is missing comment me i will send you page 6
The data set represents the total number of pencils each student in a class needs to sharpen. 0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9 which box plot correctly represents the data?
D box plot correctly represents the data
What is Box plot?A box plot or boxplot is a technique for illustratively displaying the localization, dispersion, and skewness groups of numerical data through their quartiles.
Using a five-number summary (the minimum, first quartile (Q1), median, third quartile (Q3), and "maximum"), a boxplot is a common method of visualizing data distribution.
According to the given information:The median value for the provided data will be the sixth data point's value, or 3.
The median of the data's lower half is now the first quartile. The third data point's value of 1 will therefore be in the lower quartile.
The median of the data's upper half is now referred to as the upper or third quartile. This means that the value of the ninth data point, which is 6, will represent the upper quartile.
Thus, box-plot D effectively displays the data from above.
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Answer:
The answer is D.
Edg 2023.
Help please I need this asap
Answer:
It is a little hard to see. I think that it is 10.
Step-by-step explanation:
They break even where the two lines intersect. If you look at the bottom of the graph and find 10 and then trace that straight up, I think that is where I see the lines crossing.
3 cuboids each of dimensions 4 cm x 4 cm x 6 cm and 3 cuboids each of dimensice 4 cm x 6 cm x 6 cm. A student wants to arrange these cubes and cuboids in the form of a big cube. Is it possible for him/her to arrange them in the form of a big cube? If yes, then find te length of side of new cube so formed
Step-by-step explanation:
In a Mathematics lab. There are some cubes and cuboids of following measurements
(i) One cube of side 4 cm
(ii) One cube of side 6 cm
(iii) 3 cuboids each of dimensions 4cm ×4 cm ×6cm
(iv) 3 cuboids each of dimensions 4cm ×6 cm ×6cm
A student wants to arrange these cubes and cuboids in the form of big cube. Is it
possible to arrange them in the form of big cube? If yes, then find the length of side of
i just need explanations on how to solve this. i have an upcoming test. please help.
[tex]\frac{3x}{6y} x\frac{7}{12y}[/tex]
The product of the given expression is 7x/24y²
Product of fractionsGiven the product of the fractions below
3x/6y * 7/12y
Simplify
x/2y * 7/12y
Multiply the numerator and denominator to have:
7x/24y²
Hence the product of the given expression is 7x/24y²
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Is sin(sin^-1x) = sin-1(sinx) an identity? Why or why not?
It should be noted that sin(sin^-1x) = sin-1(sinx) is not an identity.
What is identity?It should be noted that an identity simply means an equation that is always true no matter the values that are substituted.
In this case, should be noted that sin(sin^-1x) = sin-1(sinx) is not an identity. It's simply the inverse of the sine function.
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For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is
equivalent to tan A?
OX
Equivalent to tan A =[tex]\frac{y}{x}[/tex]
What is meant by the right triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. The perpendicular and the triangle's base are the sides that make up the right angle. The third side is the longest of the three sides, known as the hypotenuse.A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilize specific terminology.A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a rectangled triangle.Equivalent to tan A:
A right triangle ABC so that m∠C = 90°
The lengths are:
Side a is opposite ∠A,
Side b is opposite ∠B,
Side c (the hypotenuse) is opposite ∠C
Because cos A = x, therefore
[tex]x =\frac{b}{c}[/tex] => [tex]b = cx[/tex] (1)
Because sin A = y, therefore
[tex]y =\frac{a}{c}[/tex] => [tex]a = cy[/tex] (2)
By definition,
tan A = a/b
[tex]=\frac{cy}{cx}[/tex]
[tex]=\frac{y}{x}[/tex]
Equivalent to tan A =[tex]\frac{y}{x}[/tex]
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Find the surface area of the composite figure.
5 cm
6 cm
20 cm
4 cm
5 cm 4 cm
SA =
12 cm
-6 cm
[?] cm²
Answer:
[tex]644cm^2[/tex]
Step-by-step explanation:
First we'll work out the surface area of the pink figure.
That's the area of the two 5 by 6 rectangles on the top and bottom, plus the area of the two 5 by 20 and two 6 by 20 rectangles on the sides.
However, we note that the purple figure is blocking out a 6 by 12 section on the pink figure, so we'll need to subtract this.
The above works out to [tex]2\times(30+100+120)-72=428 cm^2[/tex].
Then we'll work out the surface area of the purple figure.
This will be the area of the two 4 by 6 rectangles at the top and bottom, plus the area of the two 4 by 12 and one 6 by 12 rectangles on the sides. Note that there's only one 6 by 12 rectangle because the other face is joined to the pink figure, so it's blocked out.
That's [tex]2\times(24+48)+72=216cm^2[/tex].
So the total surface area is [tex]428+216=644cm^2[/tex].
How many faces, edges and vertices does the shape below have?
Faces:
Edges:
Vertices:
the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.
How to determine the numberIt is important to note that according to Euler’s formula for any convex polyhedron, the number of Faces (F) and vertices (V) added together is exactly two more than the number of edges (E).
It is mathematically written as;
Face + vertices = 2 + edges
F + V = 2 + E
From the figure given, we can see that it is a kite
Number of vertices = 4
Number of faces = 4
2 + edges = faces + vertices
2 + edges = 4 + 4
2 + edges = 8
Edges = 8 - 2
Edges = 6
Thus, the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.
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Alvin and Bala had 26 stickers. Alvin had 8 more stickers than Bala. How many
stickers did Bala have?
Answer:
Bala has 5 stickers
( please mark me as brainliest )
Step-by-step explanation:
total stickers = 26
= 26/2
=13
stickers Alvin had more = 8
=13 + 8
= 21
= 26 - 21
= 5
.. . Bala has 5 stickersWhat is the end behavior of the function f of x equals negative 2 times the cube root of x?
Concluding, the end behavior is:
as x ⇒ ∞, f(x) ⇒ -∞
as x ⇒ -∞, f(x) ⇒ ∞
What is the end behavior of the given function?
Here we have the function:
[tex]f(x) = -2*\sqrt[3]{x}[/tex]
When we evaluate the function in x that tends to positive infinity, the cubic root also tends to infinity, while because of the negative factor that multiplies it, we conclude that the end behavior is:
as x ⇒ ∞, f(x) ⇒ -∞
When x tends to negative infinity, the opposite happens:
as x ⇒ -∞, f(x) ⇒ ∞
Concluding, the end behavior is:
as x ⇒ ∞, f(x) ⇒ -∞
as x ⇒ -∞, f(x) ⇒ ∞
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