The radius of the sector is 3cm and the central angle is approximately 70.53 degrees.
Now, we are given the length of the arc of the sector, which we can call "l", and the area of the sector, which we can call "A".
To find the radius, we can use the formula:
r = (l/2π) x circumference
where π (pi) is a mathematical constant approximately equal to 3.14. The circumference is the distance around the circle, which we can find using the formula:
circumference = 2πr
Combining these two formulas, we can solve for the radius:
r = (l/2π) x 2πr
r = l/2
So, the radius of the sector is half of the length of the arc. In this case, the length of the arc is given as 6cm, so the radius is:
r = 6/2
r = 3cm
Now, let's find the central angle. We can use the formula:
central angle = (area/circle area) x 360 degrees
The circle area is given by the formula:
circle area = πr²
Substituting the value of radius we obtained earlier, we can calculate the circle area as:
circle area = π(3)²
circle area = 9π
The area of the sector is given as 15cm². So, we can substitute the values of area and circle area in the formula for central angle to get:
central angle = (15/9π) x 360
central angle ≈ 70.53 degrees
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(4 x 1/10) + (8 x 1/1000) to the nearest hundredth *
.Mr. Kalada is three times as old as his son. After fifteen years, Mr. Kalada will be twice as old as his son's age at that time. Hence, Mr. Kalada's present age is
Answer:
Mr Kalada's present age is 45 years old
Step-by-step explanation:
Sawyer got a gift card for his birthday and
wants to use it for a new video game. The game
costs $60, but his gift card only covers 50% of
that. His mom agrees to cover the rest, but says
he must pay the money back in three weeks.
How much does he have to pay each week if he
pays the same amount each week?
Answer:
Sawyer has to pay $10 each week to pay his mom back
Step-by-step explanation:
Sawyer got a gift card that he wants to use to purchase a video game that costs $60, but he can only cover 50% of it, that is, $30.
The remaining $30 will be covered by his mom, given he pays the money back in three weeks.
If he pays the same amount each week, then each week he should pay $30 / 3 = $10
Sawyer has to pay $10 each week to pay his mom back
Show what a monomial expression looks like
Give me a monomial expression and solve it, step-by-step, thoroughly, show your work and explain with each step how your doing it
(New to this, thanks in advance for the extra help!!!)
Answer:
Refer to the step-by-step explanation.
Step-by-step explanation:
Come up with a monomial expression and solve it.
What is a monomial expression?A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.
Here are a few examples of an monomial expression:
5x-2xy²3a⁵7m³n²\(\hrulefill\)
Let's work with the monomial expression, 3x²y³z.
To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.
Plug these values into the expression:
3x²y³z
=> 3(3)²(2)³(1)
=> 3(9)(8)(1)
=> 27(8)(1)
=> 216(1)
=> 216
Thus, the expression is solved.
solve pls brainliest
MA.7.DP.1.4
A group of friends has been given $800 to host a party. They must decide how much money
will be spent on food, drinks, paper products, music and decorations.
Part A. As a group, develop two options for the friends to choose from regarding how to
spend their money. Decide how much to spend in each area and create a circle
graph for each option to represent your choices.
Part B. Mikel presented the circle graph below with his recommendations on how to
spend the money. How much did he choose to spend on food and drinks? How
much did he choose to spend on music?
Party Spending Proposal
Mail
17%
Paper Products
Answer: $130 money did Brenda and Hazel have all together before buying decorations and snacks.
Here, we have,
You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.
Setup
Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...
(x/2 -58) : (x/2 -37) = 1 : 4
Solution
Cross-multiplying gives ...
4(x/2 -58) = (x/2 -37)
2x -232 = x/2 -37 . . . . . . eliminate parentheses
3/2x = 195 . . . . . . . . . . . . add 232-x/2
x = (2/3)(195) = 130 . . . . . multiply by 2/3
Brenda and Hazel had $130 altogether before their purchases.
Alternate solution
The difference in their spending is $58 -37 = $21.
This is the same as the difference in their final balances.
That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.
Their ending total is 1+4 = 5 ratio units, or $35.
The total they started with is $58 +37 +35 = $130.
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complete question:
Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?
the lateral area of a cone is 10.8in squared. the radius is 2.7 in find the slant height SH=__ intype a whole number.
STEP - BY - STEP EXPLANATION
What to find?
The slant height of a cone.
Given:
lateral area = 10.8
radius = 2.7
Step 1
Recall the formula of the lateral area of a cone.
\(A_L=\pi rl\)where r is the radius and l is the slant height.
Step 2
Substitute the values into the formula.
\(10.8=3.14\times2.7\times l\)\(10.8=8.478l\)Step 3
Divide both-side of the equation by 8.478
\(l=\frac{10.8}{8.478}\)\(\approx1in\)ANSWER
SH = 1 in
1. Henry's little brother still sleeps in a crib at night. The crib is designed so the mattress can
be lowered as his brother gets older. The top and bottom pieces are parallel to one
another.
Currently, his crib is on Level 1 as shown below. If the m <2 is 42°, find the m <4 and m <7.
m<4=138°
m<7 = 42°
The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.
To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.
Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.
Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.
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f(x) = 2 - 4x
Solve for x when f(x) = 20
Answer:
x = -4.5
Step-by-step explanation:
\(20 = 2 - 4x\)
\(18 = - 4x\)
\( - 4.5 = x\)
1. Each of three friends—Lin, Jada, and Andre—had the goal of raising $40.
Lin raised 100% of her goal.
Jada raised 50% of her goal.
Andre raised 150% of his goal.
Explain your reasoning and find out how much lin raised
Answer:
Jin raised 40$ since it was his goal and he reached it
25 POINTS HELP ME ASAPPPPPPPPPPPPPPPP!!!!!!
Answer:
1/6?
Let's do it...
( (3^(3/4))/(3^(3/8)) )^4/9
According to indices rules here the denominator and numerator has the same base and they are dividing so the powers will subtract..... Its just a formulae not rocket science so don't freak out.
So ( 3^(3/4 - 3/8)) ^4/9
= ( 3^(3/8)) ^4/9
Again with indices rule the powers will multiply
Which will return us 3^1/6 which corresponds 3^x..... Hence x =1/6
Thank you
\( \boxed{ \boxed{x = \frac{1}{6} }}\)
Solution :\( \hookrightarrow \: {\bigg( \dfrac{3 {}^{ \frac{3}{4} } }{ {3}^{ \frac{3}{8} } } \bigg) }^{ \frac{4}{9} } \)
\( \hookrightarrow \: {(3 {}^{ \frac{3}{4} } \div 3 {}^{ \frac{3}{8} } ) } ^{ \frac{4}{9} } \)
\( \hookrightarrow \: {(3 {}^{ \frac{3}{4} - \frac{3}{8} } ) }^{ \frac{4}{9} } \)
\( \hookrightarrow \:{ (3 {}^{ \frac{3}{8} } ) }^{ \frac{4}{9} } \)
\( \hookrightarrow \: 3 {}^{ \frac{3}{8} \times \frac{4}{9} } \)
\( \hookrightarrow \: {3}^{ \frac{1}{6} } \)
therefore,
the required value of x is 1/6
Wayne and Sarah both leave Sacramento at noon exactly. Wayne is driving west at 40 mph, while Sarah is driving south at 70 mph. Find the rate at which the distance between them is changing at 2pm. Show all your work, include units in your answer. You do not need to simplify!
Answer:
30units because we are dealing with speed
Which one or more of the following pairs of displacements cannot be added to give a resultant displacement of 2 meters?
a) 1 m and 1 m
b) 1 m and 2 m
c) 1 m and 3 m
d) 1 m and 4 m
Answer is (d). 1m & 4 m. The magnitude of the result of P + Q is between P + Q and P - Q. The magnitude of the resultant is between 3 and 5 meters when the displacement is between 1 and 4 meters.
A resultant displacement is produced when displacement vectors are added. However, as long as two vectors have the same vector amount, any two vectors can be added. A resultant velocity is produced when two or more velocity vectors are added. A resultant force is created when two or more force vectors are joined together.
S = x^2 + y^2 is the displacement formula that results. For displacement, use the letter "S." The object is moving in two directions at once: X in the first direction and Y in the second. Y = 0 if your object only moves in one direction.
verify option 1:
(1,1) = P+Q = 1+1=2
P-Q = 1-1 =0
Resultant R = 2+0 = 2 (so, we can add this Option)
verify option 2:
(1,2) = P+Q = 1+2=3
P-Q = 1-2 =-1
R= 3-1= 2 (so, we can add this Option)
verify option 3:
(1,3) = P+Q = 1+3=4
P-Q = 3-1 = 2
R= 4-2= 2 (so, we can add this Option)
verify option 4:
(1,4) = P+Q = 1+4=5
P-Q = 1-4 = 2
R= 5-2= 3 (so, we can't add this Option)
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Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.
Answer:
They pieces are not all the same size so it wouldn't work
Step-by-step explanation:
If this helped please mark brainliest
Need help with this
The odds in favor of an event are given. Compute the probability of the event. (Enter the probability as a fraction.)
4 to 7
The probability of the event for the given odds in favor (4 to 7) is found as 4/11.
How do you calculate the probability?The inquiry provides the unusual parameters shown below: Odd = 4 to 7First, we must translate the odd into a ratio.Thus, we have the depiction shown below: odds of 4 to 7To continue solving, we must represent the ratio as a fraction.
Thus, we have the depiction shown below.
Odds ratio equals 4/7
We use the following equation to translate the aforementioned odd's expression into a probability expression.
This is displayed as
P = (Odds + 1)/(Odds).
Replace the unknown values in the equation above.
The following equation is what we have.
P = (4/7)/(4/7 + 1)
Analyze the amount
This results
P = (4/7)/(11/7)
Put the quotient in product form.
P = (4/7) * (7/11)
Evaluate
P = 4/11
Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.
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Given the linear function f(x) = −4x + 8, what is the value of x if f(x) = 24?
x = 104
x = −4
x = −8
x = −88
Answer:
The value of x = -4
Step-by-step explanation:
The given linear function is f(x) = -4x+8
We have to find the x corresponding to f(x) = 24
For our convenience, let f(x) = y
Then y = -4x + 8
This equation implies y in terms of x.
Isolating x to one side of the equation, we get,
x = (y - 8)/-4 = (8-y)/4
This equation gives x in terms of y.
So when f(x) = y = 24,
x = (8-24)/4
⇒ x = -4
Explain how a telescope with a few mirrors inside allows us to see things kilometers away
Answer:
Telescopes have several curved lenses inside that reflect on mirrors that gather light.
Step-by-step explanation:
You can find more information on NASA as well. They have very interesting explanations and photos there. :)
Sewing patterns recommend buying extra fabric in case of mistakes. Jessica bought 5 yards of fabric, plus 20% extra fabric. Deric bought 3 yards of fabric, plus 25% extra. Who bought more fabric? How much more?
Answer:
Jessica, and she bought 2 more
45 POINTS TO WHO EVER CAN SOLVE THIS QUESTION
Answer:
Step-by-step explanation:
for 5 it is the blues
Answer:
D is the answer
Step-by-step explanation:
The value of coins in the pockets of several students is recorded. What is the mean of the values: 10, 20, 35, 35, 35, 40, 45, 45, 50, 60. A. 10 cents B. 35 cents C. 37.5 cents D. 50 cents
Answer:
C. 37.5
Step-by-step explanation:
10 10 + 20 + 35 + 35 + 35 + 40 + 45 + 45 + 60 + 50=375
375÷10=37.5
The mean of the given data set 10, 20, 35, 35, 35, 40, 45, 45, 50, 60 is 37.5 so option (C) will be correct.
What is mean?The mean is the average of a data set. Mean gives us the idea of that how much amount of overall data have.
In other words, the mean is the foundation of the deviation of data from all data sets.
Mean = sum of data / Number of data
For example, if you have marks in 5 subjects like 40,45,44,46,48 then the mean will be
( 40 + 45+ 44 + 46 + 48) /5 = 44.6.
Given the data set,
10, 20, 35, 35, 35, 40, 45, 45, 50, 60
Now mean is given as
Mean = sum of data / Number of data
So,
Mean = (10+20+35+35+35+40+45+45+50+60)/10
Mean = 37.5
Hence "The mean of the given data set 10, 20, 35, 35, 35, 40, 45, 45, 50, 60 is 37.5".
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PLZ HELP FAST WILL MARK BRAINLYIST
Answer:]
Part A
A: -5:2
B: -2:5
C: 3:4
Step-by-step explanation:
Plsssssssss helpppppppppppp
Answer: It is C
Step-by-step explanation:
The slop for Kitten A is 1/4 or 4
Kitten B has a slop of 2/6 or 3 so the answer is,
C Kitten B/rate of change 4Which of the following equations satisfies that y is a function of 2?
Give your answer as a comma-separated list of the labelling letters, such as A,B,C.
A: 4cy - 61 = y + 5
B: y2 - 51 = 6
C: y = 6 -3.
D: y2 + 2y = -1
E: 1 + y = 7
F:5 - 6y +3=0
G: y = 2.-5
H: y10 = 81 - 1
Answer:
A, C, F
Step-by-step explanation:
Given:A : 4xy- 6x = y + 5
B: y^2-5x = 6
C: y^3 = 6-3x
D: y^2 + 2y =-x
E: |x+y| = 7
F: 5x - 6y + 3 = 0
G: |y| = 2x - 5
H: y^l0-8x- 1
Find:Which equations graph as a function of x.
Solution:Even-degree polynomial terms in y, and absolute-value expressions involving y can result in a given x-value being mapped to multiple y-values. When that is the case, the relation is not a function.
The relations that are functions of x are ...
A, C, F
__
The others are not, because ...
even-degree in y: B, D, Habsolute value in y: E, GWhich of the following conditions are sufficient to show that triangle ABC sim triangle QPR
Select all that apply.
A. m angle Q = 63
B. m angle R = 81
D. m angle P = 81
C. RP = 4.5
Answer:
C. RP = 4.5
Step-by-step explanation:
You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.
SimilaritySimilarity can be shown if all three sides are proportional, or if two angles are congruent.
The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.
C. RP = 4.5
__
Additional comment
The side ratios in the two triangles are ...
AB : BC : CA = 10 : 9 : 6
QP : PR : RQ = 5 : PR : 3
For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.
Two people are playing the game rock, paper scissors. In each round both players show rock, paper, or scissors at the same time. What is the probability that both players show rock in the first round. Show your work.
The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).
In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.
To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.
Therefore, the probability that both players show rock in the first round can be calculated as follows:
P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9
So the probability that both players show rock in the first round is 1/9 or approximately 0.111.
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I am stumped >:( ahhhhhhh
Answer:
\(\frac{1}{32} yards^{3}\)
Step-by-step explanation:
\(V=w*h*l\)
↓
\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)
=
\(\frac{1}{32} yards^{3}\\\)
Hope this helps!
A residential community was polling households to find out whether they wanted to get their TV signal from a satellite or cable. The results are shown in the Venn diagram.
A circle labeled satellite 55 overlaps a circle labeled cable 75. Overlap is labeled 12. 4-column table with 3 rows. First column has no label with entries satellite, not satellite, total. Second column is cable with entries blank, 51%, blank. Third column is not cable with entries a, b, blank. Fourth column is labeled total with entries blank, blank, 100%.
What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent.
a = 82%, b = 3%
a = 38%, b = 50%
a = 38%, b = 3%
a = 93%, b = 19
The correct answer is:
a = 43%
b = 88%
To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.
From the Venn diagram, we can gather the following information:
The circle labeled "satellite" has a value of 55.
The circle labeled "cable" has a value of 75.
The overlap between the two circles is labeled as 12.
Using this information, we can complete the table:
First column - "Satellite":
Entries: Satellite, Not satellite, Total
Total: 55 (as given in the Venn diagram)
Second column - "Cable":
Entries: Blank, 51%, Blank
To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).
Cable: 75 - 12 = 63
Therefore, the entry becomes: Blank, 51%, Blank
Third column - "Not Cable":
Entries: a, b, Blank
To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).
a: 55 - 12 = 43
To find the value for "b," we subtract the overlap (12) from the total number of households (100).
b: 100 - 12 = 88
Therefore, the entries become: 43, 88, Blank
Fourth column - "Total":
Entries: Blank, Blank, 100%
The total number of households is given as 100% (as stated in the question).
Therefore, the values of a and b in the relative frequency table are:
a = 43% (rounded to the nearest percent)
b = 88% (rounded to the nearest percent)
Hence, the correct answer is:
a = 43%
b = 88%
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Each bottle of perfume contains 2.1 fluid ouncens of perfumes . The store sells 30 bottles . How many fluid ounces of perfume did the store sell in totall
Answer:
63
Step-by-step explanation:
Answer: 63
Step-by-step explanation:
2.1 x 30 = 63
Find the volume of a right circular cone that has a height of 15.2 cm and a base with a diameter of 11.9 cm. Round your answer to the nearest tenth of a cubic centimeter.
9514 1404 393
Answer:
563.5 cm³
Step-by-step explanation:
Use the formula for the volume of a cone:
V = (1/3)πr²h
Recognize that the radius is half the diameter:
r = (11.9 cm)/2 = 5.95 cm
V = (1/3)π(5.95 cm)²(15.2 cm) ≈ 563.516 cm³
The volume of the cone is about 563.5 cm³.
_____
Additional comment
If you use 3.14 for the value of π, then the result will be 563.2 cm³.