Answer:
You want to set up an equation that will match the word problem. Let's call the amount of the first brand, F, and the amount of the second brand, S.
We want the total mixture to be 310mL so: F + S = 310
Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)
Now, we can solve the system of equations using substitution.
F + S = 310
.06F + .11S = .08(310)
F = 310 - S [solve 1st equation for F]
.06(310 - S) + .11S = .08(310) [substitute into 2nd equation]
18.6 -.06S +.11S = 24.8
.05S = 6.2
S = 124
F + 124 = 310 [substitute answer for S back into original equation]
F = 186
Answer: To make a 310mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.
Hope it helps!!!!!!brainliest pls!!!!!!!!Find the domain and real zeros of the given function
F(x)= 3x-5/x^2-x-12
Answer:
DOMAIN : x ∈ (-∞ , -3 )U (4 , ∞) or {x | x ∈ R where x ≠ -3 and 4}
REAL ZEROS : x = 5/3
Step-by-step explanation:
[tex]f(x) = \frac{3x -5}{x^{2} -x-12}[/tex]
factorize the bottom part
[tex]x^{2} - x - 12[/tex]
product = -12 , sum = -1 , factors = -4 and 3
[tex]x^{2} +3x-4x-12=0[/tex]
x (x + 3) - 4(x + 3) = 0
(x - 4) ( x + 3) = 0
x - 4 = 0 and x + 3 = 0
x = 4 and x = -3
for the function f(x) the domain is all real numbers ( R ) except - 3 and 4
Domain = x ∈ (-∞ , -3 )U (4 , ∞)
TO FIND THE ZEROS LET f(x) be equal to zero
[tex]0 = \frac{3x - 5}{x^{2} - x - 12}[/tex]
cross multiply
0 = 3x - 5
find x
3x = 5
[tex]x = \frac{5}{3}[/tex]
Answer the Both Question in the image using the knowledge of Volume of Solid. 50 points
Answer:
Part A
Cone
[tex]\mathsf{volume \ of \ a \ cone=\dfrac13\pi r^2h}[/tex]
(where r is the radius and h is the height)
Given:
r = ah = 2r = 2a[tex]\implies \mathsf{volume \ of \ the \ cone=\dfrac13\pi \cdot a^2\cdot2a=\dfrac23\pi a^3}[/tex]
Hemisphere
[tex]\mathsf{volume \ of \ a \ sphere=\dfrac43\pi r^3}[/tex]
[tex]\implies \mathsf{volume \ of \ a \ hemisphere=\dfrac12 \cdot\dfrac43\pi r^3=\dfrac23\pi r^3}[/tex]
Given
r = a[tex]\implies \mathsf{volume \ of \ the \ hemisphere=\dfrac23\pi a^3}[/tex]
Therefore
volume of cone with radius a = volume of hemisphere with radius a
Part B
[tex]6.82^2\times\sqrt[3]{0.005}[/tex]
Take log of base 10:
[tex]\implies \log_{10}(6.82^2\times\sqrt[3]{0.005})[/tex]
Using log law [tex]\log(a \times b)=\log a+\log b[/tex]:
[tex]\implies \log_{10}(6.82^2)+\log_{10}(\sqrt[3]{0.005})[/tex]
Using low law [tex]\log(a^b)=b \log a[/tex]
[tex]\implies 2\log_{10}(6.82)+\dfrac13\log_{10}(0.005)[/tex]
Log tables
The characteristic of the logarithm of a number is the exponent of 10 in its scientific notation.
The mantissa is found using the log tables and is always prefixed by a decimal point.
The row is the first two non-zero digits of the number, and the column is the 3rd digit of the number
Use the log tables to find [tex]\log_{10}(6.82)[/tex]:
6.82 = 6.82 × 10⁰
⇒ characteristic = 0
log table: row 68, column 2 ⇒ mantissa 8338 ⇒ 0.8338
characteristic + mantissa = 0 + 0.8338 = 0.8338
Therefore, [tex]\log_{10}(6.82)=0.8338[/tex]
Use the log tables to find [tex]\log_{10}(0.005)[/tex]:
[tex]0.005 = 5.0 \times 10^{-3}[/tex]
⇒ characteristic = -3
log table: row 50, column 0 ⇒ mantissa 6990 ⇒ 0.6990
characteristic + mantissa = -3 + 0.6990 = -2.301
Therefore, [tex]\log_{10}(0.005)=-2.301[/tex]
Therefore,
[tex]2\log_{10}(6.82)+\dfrac13\log_{10}(0.005)[/tex]
[tex]\implies 2\cdot0.8338 + \dfrac13 \cdot -2.301[/tex]
[tex]\implies 1.6676 - 0.767[/tex]
[tex]\implies 0.9006[/tex]
Therefore,
[tex]\log_{10}(6.82^2\times\sqrt[3]{0.005})=0.9006[/tex]
Using [tex]\log_{a}b=c \implies a^c=b[/tex]
[tex]\implies 6.82^2\times\sqrt[3]{0.005}=10^{0.9006}[/tex]
[tex]\implies 6.82^2\times\sqrt[3]{0.005}=7.954[/tex]
given for cone:
radius: aheight: 2avolume of cone:
[tex]\sf \rightarrow \dfrac{1}{3} \pi r^2h[/tex]
[tex]\sf \rightarrow \dfrac{1}{3} \pi (a)^2(2a)[/tex]
[tex]\sf \rightarrow \dfrac{2\pi a^3}{3}[/tex]
no metal wasted means no volume wasted while melting so volume: same.
volume of hemisphere:
[tex]\hookrightarrow \sf \dfrac{2}{3} \pi r^3[/tex]
This is equal to the volume of cone.
[tex]\hookrightarrow \sf \dfrac{2}{3} \pi r^3 = \dfrac{2\pi a^3}{3}[/tex]
[tex]\hookrightarrow \sf a^3 = r^3[/tex]
[tex]\hookrightarrow \sf a = r[/tex]
Therefore shown that radius of cone is similar to radius of hemisphere.
(b)
[tex]6.82^2 *\sqrt[3]{0.005}[/tex]
[tex]7.9535[/tex]
[tex]7.95[/tex]
Jasmine decides to put $100 in a savings account each month. The account pays 3% annual interest, compounded monthly. How much money, S, will Jasmine have after one year?
The total amount accrued, principal plus interest, with compound interest on a principal of $100.00 at a rate of 3% per year compounded 12 times per year over 1 years is $103.04.
Compound InterestGiven data
Principal = $100Rate = 3%Time = 1 yearA = P + I where
P (principal) = $100.00
I (interest) = $3.04
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 3/100
r = 0.03 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 100.00(1 + 0.03/12)^(12)(1)
A = 100.00(1 + 0.0025)^(12)
A = $103.04
Learn more about compound interest here:
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Item 1
The Diamond Rule says two factors, m and n, must multiply to get to the top number and add to get to the bottom number.
What are the possible values for m and n?
9 and 4
-9 and 4
6 and 6
-6 and -6
-6 and 6
-9 and -4
The diamond rule creates a system of equation for variables m and n
The possible values of m and n are 8 and 4 or 4 and 8
How to determine the possible values of m and n.The question is incomplete; so I will make use of the attached figure
When the diamond rule is applied to the figure, we have the following equations
[tex]mn = 32[/tex]
[tex]m + n = 12[/tex]
Make n the subject, in the second equation
[tex]n = 12 - m[/tex]
The first equation becomes
[tex](12 - m)m = 32[/tex]
Expand
[tex]12m - m^2 = 32[/tex]
Rewrite as:
[tex]-m^2 + 12m - 32 = 0[/tex]
Multiply through by -1
[tex]m^2 - 12m + 32 = 0[/tex]
Expand
[tex]m^2 - 4m - 8m + 32 = 0[/tex]
Factorize
[tex]m(m - 4) - 8(m - 4) = 0[/tex]
Factorize
[tex](m - 8)(m - 4) = 0[/tex]
Solve for m
m = 8 or m = 4
Recall that:
[tex]n = 12 - m[/tex]
So, we have:
n = 12 - 8 or n = 12 - 4
Solve
n = 4 or n = 8
Hence, the possible values of m and n are 8 and 4 or 4 and 8 (using the attached figure)
Read more about equations at:
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In a class of 50 high school juniors 32 students either play a sport or are in the marching band.
There are 22 juniors who play a sport and 16 who are in the marching band. What is the
probability that a randomly selected junior plays a sport and is in the marching band?
12%
22 + 16 = 38
38 - 32 = 6
6 / 50 = 12 / 100 = 12%
Alan, Betty, and Carol invested in a corporation in the ratio of 3:4:5 respectively. If they divide the profit of $26,100 proportionally to their investment, how much will each receive?
Answer:
Alan = $6525
Betty = $8700
Carol = $10875
Step-by-step explanation:
Ratio of Investment is:
Alan: Betty: Carol = 3:4:5
Total profit will be divided into 12 portions (3+4+5=12)
Total profit = $26,100
One portion = $26,100/12 = $2175
Alan gets = 2175*3= 6525
Betty gets =2175*4= 8700
Carol gets = 2175*5 = 10875
Find product of (6x^2 +8) (3x^2-5x+7) HELPPP
What is the value of X in the triangle
Answer:
x = 10√2
Step-by-step explanation:
Value Of X:
x² = 10² + 10²x² = 100 + 100x² = 200x = √200x = √100 × √2x = 10√2the value of x is 10√2 (A)
At a high school football game, the amount of concession items sold over the first 5 weeks of the season is shown below.
Based on the quantity of the various items sold at the concession stand, the items that show a linear relationship include:
Hot dogs.Nachos. Why are these items showing a linear relationship?Items that show a linear relationship are those that are either increasing or decreasing by the same amount overtime.
Change in Hotdogs:
= 142 - 131 = 120 - 109
= 11 = 11
Hotdogs are changing by the same amount.
Change in Soft drinks:
= 161 - 154 = 147 - 133
= 7 = 14
Change in Pretzels
= 96 - 64 = 120 - 112
= 32 = 8
Change in Nachos:
= 111 - 97 = 153 - 139
= 14 = 14
Therefore, the only items that are linear are the Hotdogs and Nachos.
Find out more on linear relationships at https://brainly.com/question/837754.
Find the measure of angle DGE
Answer:
40°
Step-by-step explanation:
m∠DGE = mDE/2 = 80/2 = 40°
How many 1/4 inches are in 2 inches? Draw a diagram to demonstrate your answer.
Answer:
8
Multiply 0.25 by 8 ⇒ 2 [tex]in.[/tex]
I hope this helps!
I need help with this
Answer:
SAS I believe or CPCTC depending if that is what you are working on.
Step-by-step explanation:
Expand. (1-4m)(m^2-3m+8) your answer should be a polynomial in standard form.
Answer:
13m²−35m+8−4m³
Step-by-step explanation:
Expand (1 − 4m)(m² − 3m + 8) by multiplying each term in the first expression by each term in the second expression.
1m² + 1 (−3m) + 1 ⋅ 8 − 4m ⋅ m² − 4m (−3m) − 4m ⋅ 8
Simplify terms.
13m²−35m+8−4m³
Which is the other endpoint of a line segment with one endpoint at (1, 3) and midpoint at (3,5)?
A. (2,4)
B. (4,4)
C. (5,7)
D. (4,8)
E. (8.16)
Answer:
C. (5,7)
Step-by-step explanation:
One endpoint at 1,3 and the midpoint at 3,5Your answer would be to as two to each the x and y of the midpoint. So the answer would be 5,7.
17. Find the value of y for which GHIJ must be a parallelogram.
Answer:
3/4
Step-by-step explanation:
Opposite sides of a parallelogram are congruent
6y +3 = 10y
3 = 4y
[tex]\frac{3}{4}[/tex] = y
What is the mean of this data set? {6, 11, 5, 2, 7} Enter your answer as a decimal in the box.
Answer:
6.2
Step-by-step explanation:
pretty sure this is the answer-- ^^
The mean of the given data set {6, 11, 5, 2, 7} is 6.2.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
We are given that;
Data set= {6, 11, 5, 2, 7}
Now,
To find the mean of a data set, you need to add up all the values and divide by the number of values.
In this case, there are 5 values in the data set: 6, 11, 5, 2 and 7.
To find the mean, follow these steps:
Add up all the values: 6 + 11 + 5 + 2 + 7 = 31
Divide by the number of values: 31 / 5 = 6.2
Therefore, by the mean the answer will be 6.2.
Learn more about mean and median;
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#SPJ3
help me use order of operations to find this awnser
Answer:
97
Step-by-step explanation:
4^2+3(37-(2*5))
4^2+3(37-10)
4^2+3(27)
16+3(27)
16+81
=97
Answer:
Step-by-step explanation:
(2*5)=10, 37-10=27, 4^2=16, 3(27)=81, 16+81= 97
In Diagram 5, POQ is the diameter of the circle with centre O .Find the area, in cm², of the shaded region. Use 22/7
Answer:
B) 236.25
Step-by-step explanation:
POQ is a diameter of circle with centre O having diameter 21 cm. Whereas radius is 21/2 cm (as radius is considered as half of the diameter).
Assume that the tip of the triangle that touches the circle is point 'N'. So,
NO = radius = 21/2 cm
At present time we have a triangle of radius or height 21/2 cm, base 21 cm is enclosed in circle of diameter 21 cm. And are asked to find the area of the remaining region or you can say asked to find area of the shaded region.
Shaded region = Area of Circle - Area of Triangle
= πr² - 1/2 × b × h
= 22/7 × 21/2 × 21/2 - 1/2 × 21 × 21/2
= 21/2 × 1/2 [ 22/7 × 21 - 21 ]
= 21/4 [ 22 × 3 - 21 ]
= 21/4 [ 66 - 21 ]
= 21/4 [ 45 ]
= 21 × 11.25
= 236.25
Hence, the area of the shaded region is 236.25 cm².
When we factor this equation the correct answer would be "-2x(7 + 6x)". But why would "2x(-7-6x)" be wrong?
Step-by-step explanation:
Although it is right,
The rule is that we stop factoring, if we can't factor out a constant that isn't 1.
In your example, we can still factor out-1.
The factorization 2x(-7-6x) is not wrong because distributing the outer 2x to each term inside gets us
2x times -7 = -14x2x times -6x = -12x^2which leads back to -14x-12x^2
Therefore, 2x(-7-6x) = -14x - 12x^2 is true.
Convention usually has us pull out the negative so the terms inside are all positive. This is just a practice done. There technically isn't any right way vs wrong way to factor, when we compare the two different factorizations. I think it's more of a subjective style than anything.
How do I do this equation
Find the total area of the irregular polygon shown? * m 11 m 36 sqm 84 sq.m 88 sqm
Answer:
100
Step-by-step explanation:
Split it into 3 different rectangles, find the area of each, and add them together.
Rectangle 1: length=11 width=4 11×4=44
Rectangle 2: length=11-9=2 width=6 2×6=12
Rectangle 3: length=11 width=4 11×4=44
44+12+44=100
what is the remainder of 14 divided by 374
MATH QUESTION SCREEN SHOT DOWN BELOW BRAINLIEST!
ITSS EASY PLEASE HELPP
i) 15 students
ii) 15 students
look at screen shoot
Answer:
3/5
108
Step-by-step explanation:
Let there are 3x goldfish, then 2x belta fish
total 3x + 2x = 5x fish
so 3x/5x = 3/5 are goldfish.
total fish = 5x = 180, so x = 180/5 = 36
The store has 3x = 3*36 = 108 goldfish.
Magan decides to research the relationship between the length in inches and the
weight of a certain species of catfish. He measures the length and weight of a number
of specimens he catches, then throws back into the water. After plotting all his data,
he draws a line of best fit. Based on the line of best fit, what would you predict to be
the length of a catfish that weighed 40 pounds?
Based on the line of best fit, the length of this catfish can be predicted to be 38 inches.
Given the following data:
Weight of catfish, x = 40 pounds.What is a line of best fit?A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.
From the graph of the data, we have the following linear equation:
[tex]y=\frac{1}{2} x+18[/tex]
Substituting the value of x, we have:
[tex]y=(\frac{1}{2} \times 40 )+18\\\\y=20+18[/tex]
y = 38 inches.
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what is the equation of -7 increased by a number n is 12
The final question on Walter's science exam was an essay question. Walter's essay
was 175 words long. This was 5 times more words than the minimum number of
required words. Which equation can be used to find n, the minimum number of
required words?
A 5 + n = 175
B 5 x 175 = n
C 175 - 5 = n
D5n = 175
Answer:
D
Step-by-step explanation:
If n=minimum number of required words and the essay is 175 words long which is 5 times more words than the minimum number of required words, you multiply n with 5 and equate to 175. To get n, you divide 175 with 5(175/5) which is 35 words.
feeding trough is in the shape of a
right triangular prism. The triangular end
of the trough measures 3 ft across and
1
is 1 4 it deep. The feeding trough is 40
feet long. How much cattle feed can the
trough hold?
Step-by-step explanation:
1 1/4
is also 5/4
5/4 * 3 * 1/2 * 40 =
answer in comments
please mark as brainest
line S is y=1/3x-3 and line T is y=-x+5. How do I graph the solutions?
Answer:
#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D
Step-by-step explanation:
#1) If the data set is linear, the slope will be constant throughout the entire data set. For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2
The slope is constant throughout the entire set. The set is also increasing; as x increases, y increases as well.
#2) Substituting 4 for y and 1 for x,
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.
#3) Since he runs 10 laps per hour t, this is 10t. Adding the first lap to this, we get y=10t+1.
#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term. If the common difference is 2, this means that 2 was added each time. This only works for choice A.
#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.
#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)
Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2
Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5
Add 5 to both sides:
6+5 = d-5+5
11 = d
#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)
Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6
Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7
#14) If two lines are parallel, they have the same slope. The slope of the given equation is 4; the only one with a slope of 4 is A.
#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped). The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2. The only one with this slope is D.
#16) The two equations are not the same, so there are not infinitely many solutions. The variables do not both cancel, so there is at least one solution. This only leaves one solution as the answer.
#19) Using 1 for 7 and 4 for x, we check each equation. The only one that comes out correct is D.
i hope this work for you
and sory if im wrang