Answer:
120 kg of 30% fat-content chocolate and 30 kg of 40% fat-content chocolate.
Step-by-step explanation:
We are given that a candy distributor needs to mix a 30% fat-content chocolate with a 40% fat-content chocolate to create 150 kilograms of a 32% fat-content chocolate.
Let the amount of 30% fat-content chocolate be 'x' and the amount of 40% fat-content chocolate be 'y'.
So, according to the question;
x + y = 150 ------------ [equation 1]
and [tex]30\% \text{ of } x + 40\% \text{ of } y=32\% \text{ of } 150[/tex]
[tex]30x+40y= 32 \times 150[/tex]
[tex]30x+40\times (150-x)= 4800[/tex]
[tex]30x+6000-40x= 4800[/tex]
[tex]10x = 6000-4800[/tex]
[tex]x=\frac{1200}{10}[/tex]
x = 120 kg
Now, putting the value of x in equation 1, we get;
x + y = 150
120 + y = 150
y = 30 kg
Hence, 120 kg of 30% fat-content chocolate and 30 kg of 40% fat-content chocolate.
What is the scale factor from Figure 2 to Figure 1?
Answer:
3
Step-by-step explanation:
Each of the lines lengths multiply by 3.
Suppose line segment AB has one endpoint at A(0, 0). What are the coordinates of B if (5, 3) is 1/3 of the way from A to B?
Answer:
[tex]B(x_2,y_2)= (20,12)[/tex]
Step-by-step explanation:
Given
[tex]A = (0,0)[/tex]
[tex]Ratio; m : n = 1 : 3[/tex]
[tex]Point\ at\ 1 : 3 = (5,3)[/tex]
Required
Coordinates of B
This question will be answered using line ratio formula;
[tex](x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]
In this case:
[tex](x,y) = (5,3)[/tex]
[tex](x_1,y_1) = (0,0)[/tex]
[tex]m : n = 1 : 3[/tex]
Solving for [tex](x_2,y_2)[/tex]
[tex](x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex] becomes
[tex](5,3) = (\frac{1 * x_2 + 3 * 0}{1 + 3},\frac{1 * y_2 + 3 * 0}{1 + 3})[/tex]
[tex](5,3) = (\frac{x_2 + 0}{4},\frac{y_2 + 0}{4})[/tex]
[tex](5,3) = (\frac{x_2}{4},\frac{y_2}{4})[/tex]
Comparing the right hand side to the left;
[tex]\frac{x_2}{4} = 5[/tex] -- (1)
[tex]\frac{y_2}{4} = 3[/tex] -- (2)
Solving (1)
[tex]x_2 = 5 * 4[/tex]
[tex]x_2 = 20[/tex]
Solving (2)
[tex]y_2 = 3 * 4[/tex]
[tex]y_2 = 12[/tex]
Hence;
[tex]B(x_2,y_2)= (20,12)[/tex]
PLEASE HELP! 40 points!! I've been stuck on this for 30 minutes constantly coming up with all different answers, please help me.
What is the area of rhombus ABCD?
Enter your answer in the box. Do not round at any steps.
______units²
Answer:
36 units^2
Step-by-step explanation:
The area of a triangle is 1/2*base*height. Knowing this is just 2 triangles means you solve for 1 triangle, then multiply that by 2
Answer:
[tex]A=36\text{ units}^2[/tex]
Step-by-step explanation:
The area of a rhombus is given by the formula:
[tex]A=\frac{d_1\cdot d_2}{2}[/tex]
Namely, it is half of one diagonal multiplied by the other diagonal.
So, to find the area, we just need to find the length of AC and BD, multiply them together, and then divide by 2.
To find their lengths, we can use the distance formula. The distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
So, let's find the lengths of each diagonal:
AC:
Point A is (-1,0) and Point C is (-1,-6). Let (-1,0) be (x₁, y₁) and let (-1,-6) be (x₂, y₂). Substitute this into our formula:
[tex]d=\sqrt{(-1-(-1))^2+(-6-0)^2[/tex]
Simplify:
[tex]d=\sqrt{(-1+1)^2+(-6-0)^2[/tex]
Add or subtract:
[tex]d=\sqrt{(0)^2+(-6)^2[/tex]
Square:
[tex]d=\sqrt{36}[/tex]
Take the square root:
[tex]d=6[/tex]
So, the length of diagonal AC is 6.
BD:
Point B is at (5,-3) and Point D is at (-7,-3). Let (5,-3) be (x₁, y₁) and let (-7,-3) be (x₂, y₂). Substitute this into our formula:
[tex]d=\sqrt{(-7-5)^2+(-3-(-3))^2[/tex]
Simplify:
[tex]d=\sqrt{(-7-5)^2+(-3+3)^2[/tex]
Add or subtract:
[tex]d=\sqrt{(-12)^2+(0)^2[/tex]
Square:
[tex]d=\sqrt{144}[/tex]
Take the square root:
[tex]d=12[/tex]
So, our second diagonal is 12 units long.
Now, to find the area, substitute 6 and 12 into our formula. So:
[tex]A=\frac{d_1\cdot d_2}{2}[/tex]
Substitute 6 for d₁ and 12 for d₂. So:
[tex]A=\frac{(6)(12)}{2}[/tex]
Multiply:
[tex]A=\frac{72}{2}[/tex]
Divide:
[tex]A=36\text{ units}^2[/tex]
So, the area of the rhombus is 36 squared units.
And we're done!
Notes:
Of course, instead of using the distance formula, you can also just count :)
Help!! Need Some Homework Help ASAP!
Answer:
175°
Step-by-step explanation:
Since, [tex] \overrightarrow{BD} [/tex] is in the interior of [tex] \angle ABC[/tex]
[tex] \therefore m\angle ABC = m\angle ABD + m\angle CBD\\
\therefore (14x + 21)\degree = (2x + 3)\degree + 150\degree \\
\therefore (14x + 21)\degree = (2x + 153)\degree\\
\therefore 14x + 21 = 2x + 153\\
\therefore 14x - 2x = 153 - 21\\
\therefore 12x = 132\\
\therefore x = \frac{132}{12}\\
\therefore x = 11\\\\
m\angle ABC = (14x + 21)\degree\\
m\angle ABC = (14\times 11+ 21)\degree\\
m\angle ABC = (154+ 21)\degree\\
\huge\red {\boxed {m\angle ABC = 175\degree}} \\[/tex]
Complete each ratio table to solve each problem.
11 To make 5 apple pies, you need about 2 pounds
of apples. How many pounds of apples do you need
to make 20 apple pies?
Answer:8 pounds to make 20 apple pies
Find the area of the surface given by z = f(x, y) over the region R. (Hint: Some of the integrals are simpler in polar coordinates.) f(x, y) = 9 − x2 R: square with vertices (0, 0), (2, 0), (0, 2), (2, 2)
Answer:
The area of the surface over R is [tex]\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]
Step-by-step explanation:
From this study,
The surface area of f(x,y) is expressed by:
[tex]A = \iint_R \sqrt{1 +f^2_x+f^2_y}} \ dA[/tex]
where
[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 2[/tex]
Given that:
f(x,y) = 9 - x²
Thus, [tex]f_x = -2x[/tex] and [tex]f_y = 0[/tex]
However, the area becomes:
[tex]A = \iint_R \sqrt{1+(-2x)^2+0^2} \ dxdy[/tex]
[tex]A = \iint_R \sqrt{1+4x^2} \ dxdy[/tex]
From above, replacing x with [tex]\dfrac{1}{2} \ tan \ u[/tex]
then [tex]dx = \dfrac{1}{2} sec^2 \ udu[/tex]
∴
[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint \sqrt{1 + 4u^2 } \ sec^2 \ udu[/tex]
[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint sec^2 \ udu[/tex]
[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} ( \sqrt{4x^2 + 1x} + \dfrac{1}{2} In \sqrt{4x^2 + 1}+2x)[/tex]
Hence;
[tex]\mathsf{A = \int \limits ^2_0 \begin {bmatrix} \dfrac{1}{2}(\sqrt{4x^2 +1 x}+ \dfrac{1}{2} In ( \sqrt{4x^2+1}+2x \end {bmatrix}^2_0 \ dy}[/tex]
[tex]\mathbf{A = 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]
Therefore, the area of the surface over R is [tex]\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]
1) round 24,837,618 to the ten thousands place.
I need help on my college math pls help me it needs to be shown work on paper!
Answer:
24,840,000
Step-by-step explanation:
The number in the ten thousands place is 3. The number to the right of it is 7. Since 7 ≥ 5, we round up the 3 to a 4.
24,837,618 ≈ 24,840,000
I am a three digit number. I am greater than 312 but less than 348. The digit in my tens place equals 5+2. The sum of my digits is 18. What number am I?
Ted is looking over his spending pattern for the past week to try to determine how much money he had on Sunday. This is Ted's spending pattern: Day Debit ($) Credit ($) Monday 112 --- Tuesday 141 18 Wednesday 56 --- Thursday 28 70 Friday 22 42 Saturday 16 88 If the bank charges Ted an overdraft fee of $25 every time he overdraws his account, and Ted overdrew his account on Wednesday but not on Friday, which of the following is a possible amount of money that Ted could have had in his account last Sunday? Assume that the only debits and credits not listed are overdraft fees. a. $300 b. $280 c. $240 d. $200
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Consider a problem where we are rolling 2 dices where each dice has 6 faces numbered from 1 to 6.Answer the following questions:(1) What is the sample space?(2) If the event we are interested in is the sum being 10, what would be the probability of observingsuch an event?(3) If the event we are interested in is the sum being 6, what would be the probability of observingsuch an event?
Answer:
1. See Explanation for Sample Space
2. [tex]P(10) = \frac{1}{12}[/tex]
3. [tex]P(6) = \frac{5}{36}[/tex]
Step-by-step explanation:
Given
Roll of Two die
Solving (1): The Sample Space
Represent the first dice with S1 and the second with S2
[tex]S_1 = \{1,2,3,4,5,6\}[/tex]
[tex]S_2 = \{1,2,3,4,5,6\}[/tex]
The sample space of both die is:
[tex]S = (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)[/tex][tex](4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(55,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}\}[/tex]
Solving (2): Probability of Sum being 10
First, we need to add the outcome of each roll in (1) above:
[tex]S = \{2,3,4,5,6,7, 3,4,5,6,7,8, 4,5,6,7,8,9, 5,6,7,8,9,10, 6,7,8,9,10,11 7,8,9,10,11,12\}[/tex][tex]n(S) = 36[/tex]
[tex]n(10) = 3[/tex]
The required probability is:
[tex]P(10)= \frac{3}{36}[/tex]
[tex]P(10) = \frac{1}{12}[/tex]
Solving (3): Probability of Sum being 6
[tex]n(S) = 36[/tex]
[tex]n(6) = 5[/tex]
The required probability is:
[tex]P(6) = \frac{5}{36}[/tex]
Evaluate the expression and enter your answer in the box below.
-7 • (5+ 3) +216 ➗ 4
Answer:
= -2
-7(5+3)+216/4
-7(8)+216/4
-56+54
= -2
what appear to be the next two terms in this sequence
18, 24, 32, 128/3.....
Answer: 512/9 and 6,144/81
Step-by-step explanation:
The sequence is:
18, 24, 32, 128/3, ...
Now, is easy to see that it is not an arithmetic sequence, so we can jump to see if this is a geometric sequence.
To see this, we must see at the quotient of two consecutive numbers in the sequence, and that quotient must be the same for any pair of consecutive elements.
24/18 = 1.33...
32/24 = 1.33...
(128/3)/32 = 1.33....
The quotient is constant, then this is a geometric sequence.
Then we can write the n-th term as:
Aₙ = Aₙ₋₁*1.33...
And we first should write 1.33 in a way that is easier to use:
1.33... = 1 + 0.33...
The left side can be writen as:
0.33... = 0.33...*(10/10) = (3.3.../10)
Now we can subtract the initial number:
(3.33..../10) - 0.33... = 3/10 = 0.33...*(9/10)
0.33... = (3*10)/(9*10) = 30/90 = 3/9
then we have:
1.33... = (1 + 3/9) = (9/9 + 3/9) = (12/9)
Then the two next terms are:
(128/3)*(12/9) = 128*4/9 = (512/9)
And the next term is:
(512/9)*(12/9) = (6,144/81)
Then the first six terms are:
18, 24, 32, 128/3, 512/9, 6,144/81
$1,672.68
$287.84
$12.32
Answer:
$1672.68
Step-by-step explanation:
a regular polygon has 20 sides the measure of an exterior angle of polygon is
Answer:
198 degrees
Step-by-step explanation:
Such a shape is called a 20-gon, such shapes have an interior angle of 162. Hence, the exterior angle = 360 (Complete angle) - 162 (The interior anlge) = 198 degrees, Hope my answer helps you, Thank you, and please add me as brainliest! Thanks
Answer:
Step-by-step explanation:
Such a shape is called a 20-gon, such shapes have an interior angle of 162. Hence, the exterior angle = 360 (Complete angle) - 162 (The interior anlge) = 198 degrees, Hope my answer helps you, Thank you, and please add me as brainliest! Thanks and Godbless
A group of 7 students was asked, "How many hours did you watch television last week?" Here are their responses. 20,6,17,10,19,15,9 Find the mean number of hours for these students. If necessary, round your answer to the nearest tenth.
Answer: 13.71
Step-by-step explanation:
20+6+17+10+19+15+9=96
96/7=13.71
Find the value of B
Answer:
34
Step-by-step explanation:
b+115°+31°= 180° (sumof all angles of triangle)
b=146°-180°
b=34°
hope it helps you!
steffie matt
Solve this linear system 28x + 44y = 964.40 21x + 33y = 723.30
28x + 44y = 964.40
21x + 33y = 723.30
Let's multiply the first equation by 4 and the second by -4
84x + 176y = 3857.6
-84x - 132y = -2893.2
Add the equations together.
0 + 44y = 964.4
Simplify
44y = 964.4
Divide both sides by 44
y = 964.4/44
Since we have the value of y, let's plug 964.4/44 into y for the first equation.
28x + 44(964.4/44) = 964.40
Simplify the left side
28x + 964.4 = 964.4
Subtract 964.4 from both sides
28x = 0
Divide both sides by 0
x = 0
In conclusion,
y = 964.4/44
x = 0
Five numbers has a mean of 12. When one (1) number is removed the mean is 11. What is the value of the number removed?
Answer:
16
Step-by-step explanation:
The mean of a group of values is calculated as
mean = [tex]\frac{sum}{count}[/tex]
Given 5 numbers with a mean of 12, then
[tex]\frac{sum}{5}[/tex] = 12 ( multiply both sides by 5 )
sum = 60
let the number removed be x , then
[tex]\frac{60-x}{4}[/tex] = 11 ( multiply both sides by 4 )
60 - x = 44 ( subtract 60 from both sides )
- x = - 16 ( multiply both sides by - 1 )
x = 16
The number removed was 16
Nicole and her children went into a grocery store and she bought $6 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. She bought 4 times as many bananas as apples. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Nicole bought.
a right rectangular prism has these dimensions:
Length: 1 1/3
width: 5/6
height: 2/3
Between 9 P.M. and 6:54 A.M., the water level in a swimming pool decreased by in. Assuming that the water level decreased at a constant rate, how
50
much did the water level drop each hour?
I think the question is incorrect please repeat again.....
The product of 2 and the sum of a number and 8 is equivalent to 16.
Which equation models this sentence?
x = some unknown number
x+8 = sum of the number and 8
2(x+8) = product of 2 and the sum of a number and 8
2(x+8) = 16 is the final answer1. Which relations are functions?
1.
III.
ty
II.
IV.
A II and III
BI and II
III and IV
0 Iand IV
Answer:
please put the full question
Round 89678 to the nearest hundredth thousand
Answer:
100,000
Step-by-step explanation:
89678 rounded to the nearest hundred thousand is 100,000.
Christine runs 4 miles in 30 minutes. At the same rate, how many miles would she run in 48 minutes?
Answer:
she would run 6.4 miles in 48 min
Step-by-step explanation:
hope it helps
What are the two solutions of 2x2 = –x2 – 5x – 1?
Answer:
x=1+√334, x=1−√334
Step-by-step explanation:
ANSWER is C on edge for those of you looking
Step-by-step explanation:
How do you solve the equation -x/3=27
QUESTION 7
A patient's surgery is scheduled for 1500 hours. The patient must register two hours before the surgery. At what STANDARD time should the patient arrive to register? Be sure to
indicate AM or PM in your answer
Answer:
1:00 PM
Step-by-step explanation:
1500 hours is 3 PM. 3-2 = 1 So that would be 1 o'clock PM.
Brian finished his English assignments in 1/3 hours. Then he completed his math assignments in 1/5 hours. What was the total number of Time Brian spent doing these two assignments
Answer: 8/15
Step-by-step explanation: find the LCD which is 15 in this case, then multiply 1/3 by 5/5 which equals 5/15. then multiply 1/5 by 3/3 which equals 3/15 then add them together =8/15
Is -(5/12) equal to 5/-12
Answer:
Yes it is.
Step-by-step explanation:
-(5/12) = -*5/12 = -5/12
5/-12 = -5/12
Best of Luck!