The ratio of the number of cherry tomatoes in a tossed salad to people served is 7:15. If Waldo wants to serve 105 people, how many cherry tomatoes will Waldo use
Answer: 49 cherry tomatoes.
Step-by-step explanation:
7 x
— = — cross multiply and done.
15 105
A bank loaned out $19,000, part of it at the rate of 7% per year and the rest at 15% per year. If the interest received i. 1 year totaled $2000, how much was loaned at 7%
Answer:
$28571.43 was loaned out.
Step-by-step explanation:
2000 x 100 / 7=28571.43
Answer:
$28571.43 was loaned.
this is because
2000 x 100 / 7
=28571.43
What is the lateral area of the cone?Round nearest whole, round all intermediate values to four decimals.
To answer this question, we can use the next formula to find the lateral area of the cone:
\(A_L=\pi r\sqrt[]{h^2+r^2}\)Where:
• π is approximately 3.1415926535...
,• r = D/2. We have that the diameter is 6ft.
,• h = height. In this case, we have h = 7ft.
We have a right circular cone, and we can use the above formula. Then, we have:
\(D=6ft\Rightarrow r=\frac{D}{2}\Rightarrow r=\frac{6ft}{2}\Rightarrow r=3ft\)Then, we have:
\(A_L=\pi\cdot3\cdot\sqrt[]{7^2+3^2}\Rightarrow A_L=\pi\cdot3\cdot\sqrt[]{49+9}=\pi\cdot3\cdot\sqrt[]{58}\)\(\sqrt{58}=7.61577310586\approx7.6158\)Then:
\(undefined\)An equation of a circle is given as (x + 6)2 + (y − 7)2 = 81. Find the center and radius of the circle.
The equation of a circle is written as (x – h)^2 + (y – k)^2 = r^2
h and k are the center point and r is the radius.
In the given equation h = -6 and k = 7 and r would be the square root of 81, which is 9.
Center (-6,7)
Radius = 9
The required center is \((-6,7)\) and the radius is 9 units.
Given equation is,
\((x + 6)^2 + (y-7)^2 = 81\)....(1)
Equation of the circle: The general equation of the circle with the center (a,b) and the radius r is represented by,
\((x-a)^2+(y-b)^2=r^2\)...(2)
We can write the given equation as,
\((x + 6)^2 + (y-7)^2 = (9)^2\)
Comparing equations (1) and (2) we get,
The Centre of the given circle is \((-6,7)\)
The radius of the given circle is 9 units.
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CAN SOMEONE HELP ME I NEED IT NOWW PLSSSS THE QUESTIONS ARE:
1) what is the exact length of the line segment
2) find the decimal approximation of the length
PLSSS I NEED HELPPPP
Consider the following "generic rectangle" where the area of each region is given. Write equivalent
expressions that express the area of the whole rectangle as a sum and as a product.
Answer:
sum: 3x² -4x -4product: (x -2)(3x +2)Step-by-step explanation:
The areas of four regions are given. We can simply add them to find the sum. To express them as a product, we need to look at common factors.
SumThe total of the given area expressions is ...
3x² +2x -6x -4 = 3x² -4x -4 . . . . sum
ProductExtending the table to show common factors of each row and column, we have ...
\(\begin{array}{c|c|c|}&3x&2\\\cline{1-3}x&3x^2&2x\\\cline{1-3}-2&-6x&-4\\\cline{1-3}\end{array}\)
Since each cell of the table is the product of the corresponding common factors, we can write the area as the product ...
(x -2)(3x +2) . . . . product
Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children: (a) What is the probability of getting one child of each sex?
Answer:
49.97% probability of getting one child of each sex
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The sex of a children is independent of other children, so we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
The probability that a couple’s first child is a boy is 0.512.
This means that \(p = 0.512\)
The will have two children:
This means that \(n = 2\)
(a) What is the probability of getting one child of each sex?
This is P(X = 1).
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 1) = C_{2,1}.(0.512)^{1}.(0.488)^{1} = 0.4997\)
49.97% probability of getting one child of each sex
I will give you the brainliest!!! And 25 points!!!!
Someone solve this for me with explanation please. I need help
The perimeter of the given triangle with given lengths is; 78
What is the perimeter of the triangle?The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.
Now, we are given the triangle as QRS.
We are given that;
A is the midpoint of QR
B is the midpoint of RS
C is the midpoint of SQ
Thus;
QA = RA = 10
BR = SB = 15
SQ = 28
Thus;
Perimeter of Triangle = 2(10) + 2(15) + 28 = 78
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PLZ HELP ASAP!!! What is the area of sector DEF in terms of pi ?
120°
3 cm
E
Answer:
Area of the sector : D.
3π cm²
What's solid figure could be formed from the net shown 15 cm 9 cm
Answer:
triangular pyramid
..................
Find the height of the tower using the information given in the illustration.
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr
Suppose the weekly amount of money spent on maintenance and repairs by a company is NOT approximately normally distributed. However, its mean and standard deviation are known to be $400 and $20, respectively. If $450 is budgeted for next week, what can you say about the probability that the actual costs will exceed the budgeted amount
Answer:
Probability = 0.00621
Step-by-step explanation:
We are given;
Population mean; μ = 400
Population standard deviation; σ = 20
Raw score; x¯ = 450
the probability that the actual costs will exceed the budgeted amount will be the p-value.
Thus, let's first find the z-score after which we will find the p-value.
z = (x¯ - μ)/σ
z = (450 - 400)/20
z = 50/20
z = 2.5
From online p-value from z-score calculator attached, using z = 2.5; one tailed hypothesis; significance level of 0.05, we have;
P-value = 0.00621
Question 7 of 10 Is the graph increasing, decreasing, or constant? A. Constant B. Decreasing C. Increasing
Answer:
option b decreasing is your answer
The length of a rectangle is six times its width. If the rectangle is 600 yd^2 find its perimeter
Answer:
8400 yd^2
Step-by-step explanation:
600x 6 because its six times
3600
L+L+W+W=p
8400 yd ^2
Find the arithmetic mean of the following numbers -5, 12, 24, 46, 60
Answer:
27.4
Step-by-step explanation:
To find the mean of these numbers, we'll add them together, then divide by how many numbers there are.
\(\frac{-5+12+24+46+60}{5}\\\\=\frac{137}{5}\\\\=27.4\)
\(\huge{\purple{\underline{\underline{\bf{\pink{ANSWER:-}}}}}}\)
Arithmetic mean is also called as average mean. This is given by the summation of no.s present to how many no.s there are.
Calculating arithmetic mean gives,
\(:\implies\sf{ \frac{ - 5 + 12 + 24 + 46 + 60}{5} }\)\(:\implies\sf{ \frac{ - 5 + 142}{5} }\)\(:\implies\sf{ \frac{137}{5} }\)\(:\implies\sf{27.4}\)The arithmetic mean of the above given no.s is 27.4Find the volume of the sphere. Use 3.14 for n. Round to the nearest tenth. radius= 6ft.
B) What is the cost of making 35 items?
And c. The domain
The cost of making 35 items is 1100 and the domain is (-∞,∞)
The cost of making 35 items :
x = 35plug the value into the cost equation
C(35) = 10(35) + 800
C(35) = 350 + 800
C(35) = 1100
Hence, cost of making 35 items is 1100
The domain of the functionSince the value of X can be any real number, we can plug in any real number for x and get a real number output.
Hence, the domain = (-∞,∞)
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if the area of a circle is 36 x 3.14 inches squared find its diameter
Answer:
36
Step-by-step explanation:
36 x 3.14 = 113.04
Since to find a diameter from the area, you need to divide by 3.14
113.04 divided by 3.14 = 36
But since its already there you can just figure out that 36 is the diameter and you don't have to do any calculating
For triangle ABC (shown here), the value of angle BCD is equal to 30 degrees. If CD is the height of the triangle and is 12 centimeters, then what is the perimeter of triangle ABC?
The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.
What is the perimeter?
The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.
Let's call the length of AB x and the length of BC y.
First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:
Area of triangle ABC = 1/2 * CD * AB
Substituting the given values, we have:
1/2 * 12 * x = 6x
So the area of triangle ABC is 6x square centimeters.
We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:
tan(30) = x/y
Simplifying, we get:
y = x/tan(30) = x/(1/√(3)) = √(3) * x
Now we can use the formula for the area of a triangle in terms of its sides:
Area of triangle ABC = 1/2 * AB * BC * sin(B)
where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:
Area of triangle ABC = 1/2 * x * √3 * x * sin(60)
Simplifying, we get:
Area of triangle ABC = 1/4 * √3 * x²
Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:
6x = 1/4 * √(3) * x²
Multiplying both sides by 4/√3, we get:
24/√(3) * x = x²
Simplifying, we get:
x² - 24/√(3) * x = 0
Using the quadratic formula, we get:
x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1
Simplifying, we get:
x = 16√(3) / 3 or x = 8 √(3) / 3
Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:
y = √(3) * x
Therefore, we have two possible triangles:
Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3
Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3
The perimeter of each triangle is the sum of its side lengths. Therefore:
Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm
Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm
hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.
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Question 2 of 39
Look at this series: 56, 54, 50, 38, 34, ... What number should come next?
A) 23
B) 18
C) 20
D) 32
E) 26
Answer:
D) 32
Step-by-step explanation:
Given;
series: 56, 54, 50, 38, 34, ....
find the difference between successive numbers;
56 54 50 38 34 x
2 4 12 4 2
The highest difference between the numbers is 12, after which it decreases to 4 and finally back 2.
The next number "x" is calculated as;
34 - 2 = x
34 - 2 = x
32 = x
Therefore, the next number should be 32.
The next number that should come next in the series is 32.
Sequence is an arrangement of two or more things in a successive order. Series is the cumulative sum of a given sequence of terms.
Given the numbers in the series: 56, 54, 50, 38, 34, . . ..
The difference is 2, 4, 12, 4, 2
The highest difference between the numbers is 12, after which it decreases to 4 and finally back 2. Hence:
The next number = 34 - 2 = 32
The next number that should come next in the series is 32.
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I would really appreciate it if anyone could do it I can’t get help because my parents are fighting rn
Answer:
you are correct. the right answer is a. 0.96
Step-by-step explanation:
i am so sorry your parents are fighting, i know how it feels
Answer:
Step-by-step explanation:
We know that the formula for the circumference of a circle is 2πr. We know that 2 times the radius is the diameter. So, 2πr = πd. We know that a quarter of the circle's circumference is 2.88 and that π is 3. From this, we can make the equation 3d=2.88.
3d=2.88
We can divide by 3 on both sides of the equation.
d=0.96
which of the following statements is true about the solution of the system? 2x-y=8 and y=2x-3
Answer:
no roots.
Step-by-step explanation:
\(\left \{ {{2x-y=8} \atop {y=2x-3}} \right. \ = > \ \left \{ {{2x-y=8} \atop {2x-y=3}} \right. \ = > \ no \ solution.\)
What is the surface area of a sphere with a radius of nine units In pie
\(\textit{surface area of a sphere}\\\\ SA = 4\pi r^2~~ \begin{cases} r= radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies SA=4\pi (9)^2\implies SA=324\pi\)
Find the 15th term of the geometric sequence 1, -4, 16, ...1,−4,16,
Answer:
Doesn't look like a geometric sequence.
Step-by-step explanation:
If 1, -4, 16 keeps repeating then the answer is 16.
Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters as dimes. Write a system of equations that could be used to determine the number of dimes and the number of quarters that Sophie has.
Answer:
0.25q +0.10d = 4.20q = 2dStep-by-step explanation:
Let q represent the number of quarters, and d represent the number of dimes.
0.25q +0.10d = 4.20 . . . . . the value of the coins
q = 2d . . . . . . . . . . . . . . . the relation between the numbers of coins.
__
Additional comment
Using substitution, the equation simplifies to ...
0.60d = 4.20
d = 7
q = 14
Note that the coins can be grouped into groups of 2 quarters and 1 dime. The value of the group is $0.60, and the number of dimes is equal to the number of groups. Thinking about the problem in this way gets you immediately to the single equation 0.60d = 4.20.
Two pounds of cashews cost $19, and 8 pounds cost $76.
Number of pounds 2 3 8
Cost ($) 19 28.50 76
Is the relationship between the cost and the number of pounds of cashews a proportional relationship? Explain.
How can you use your equation to find the cost of 6 pounds of cashews?
Would it be possible to prove this is proportional or not proportional without the table? Explain how you know.
Please reply quickly thanks : )
Answer:
Yes there is a proportinal relationship because when I did 19 divided by 2 I got 9.5 and when I do 76 divided by 8 I got 9.5 so its proportinal. Yes I can find how much money 6 pounds is its 57. And yes I can do it without a table because all you have to do is divide the 19 and 2 and the other 2 numbers and if there the same then its proportinal.
Step-by-step explanation:
BRAINLIEST MAYBE???
Սալյումս.. 1:2 a4|0S
What is the value of 0.6 - (0.7)(1.4)
Answer:
-0.38
Step-by-step explanation:
0.6-(0.7)(1.4)
0.6-0.98
-0.38
Question 12(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $136.45 and earn $35.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
35.5 + 136.45w = 455.95; w = 9
35.5w + 136.45 = 455.95; w = 9
35.5w − 136.45 = 455.95; w = 17
35.5w − 455.95 = 136.45; w = 17
The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 , the correct option is (b) .
In the question ,
it is given that
the cost of the gaming chair = $455.95
amount of money already saved for the gaming chair = $136.45
amount of money earned by baby sitting each week = $35.50 .
let the number of weeks required to baby sit is " w " .
the equation can be represented by
cost of chair = money saved + money earned in w weeks
Substituting the values from above ,
we get
455.95 = 136.45 + 35.5w
On solving further ,
136.45 + 35.5w = 455.95
35.52w = 455.95 - 136.45
35.52w = 319.5
w = 319.5 / 35.52
w = 8.99
w ≈ 9
the number of weeks = 9
Therefore , The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 .
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if a1=5 and an=nan-1-4 then find the value if a3
EXPLANATION
If a_1 = 5 and a_n = n*a_n-1 - 4 the value of a_3 is given by the following relationship:
\(a_2=\text{ 2}\cdot5\text{ - 4 = 10-4=6}\)\(a_3=2\cdot6-4=12-4=8\)The answer is 8