Answer:
z = 10
Step-by-step explanation:
Distribute 2 to the terms in the parentheses:
2(2z + 5) = 50
4z + 10 = 50
Subtract 10 from both sides
4z = 40
Divide each side by 4
z = 10
So, the answer is z = 10
Answer:
10
Step-by-step explanation:
1. Factorize left side.
2*2z+2*5=50
4z+10=50
2. Subtract 10 from both sides
4z=50-10
4z=40
3. Divide both sides by 4
z=40/4
z=10
An actor, Bob, wants to gain weight to look the part for his role as an overweight truck driver in an upcoming movie. He decides to add servings of banana splits (S) and bacon rolls (B) to his diet. Each serving of S is 1,000 calories and each serving of B is 500 calories. Bob has a history of health problems and his doctor has recommended that he needs to control his cholesterol and sugar levels in his food intake. Each serving of S contains 1 unit of cholesterol and 3 units of sugar. Each serving of B contains 4 units of cholesterol and 1 units of sugar. His doctor recommends that his cholesterol be no larger than 10 units and his sugar levels should be at least 2 units and no larger than 9 units. What should be the objective function (C) to select the optimal choice of Sand B in order for Bob to ingest as many calories as possible? A. C = 105 + 5B B. C = 1000S + 500B C. C = S+BD. None of the above
Answer:
[tex]C = 1000S + 500B[/tex]
Step-by-step explanation:
Given
[tex]S = Banana\ Splits[/tex]
[tex]B=Bacon\ Rolls[/tex]
Reading through the question, we have:
Number of calories per serving:
[tex]S \to 1000[/tex]
[tex]B \to 500[/tex]
Let
[tex]x = Cholesterol[/tex]
[tex]y =Sugar[/tex]
So, we have:
Each serving of S
[tex]x \to 1S[/tex]
[tex]y \to 3S[/tex]
Each serving of B
[tex]x \to 4B[/tex]
[tex]y \to 1B[/tex]
Recommendation
[tex]x \to \le 10[/tex] - i.e. not more than 10 units of cholesterol
[tex]y \to \ge 2 \& \le 9[/tex] i.e. At least 2units but not more than 9 units of sugar
So, the constraints are:
[tex]S + 4B \le 10[/tex]
[tex]3S + B \ge 2[/tex]
[tex]3S + B \le 9[/tex]
Recall that the calories per serving is:
[tex]S \to 1000[/tex]
[tex]B \to 500[/tex]
Hence, the objective function is:
[tex]C = 1000S + 500B[/tex]
Help as soon as possible
A triangle has an angle that measures 50 degrees. the other two angles are in a ratio of 3:10. What are the measures of those two angles
Answer:
100 degrees, 30 degrees
Step-by-step explanation:
Write an expression for the measures of the other two angles:
one angle = 3x
other angle = 10x
These are in the ratio 3:10, but you don't know the value of x YET!
Fact: all 3 angles sum to 180 degrees.
50 + 3x + 10x = 180
50 + 13x = 180
13x = 130
x = 10
Now plug this value into the two expressions for the angle measures.
one angle = 3(10) = 30 degrees
other angle = 10(10) = 100 degrees
PLEASE HELP ILL GIVE BRAINLIEST, DIFFICULT ALGEBRA
Each graph below shows a relationship between x and y. For each graph, determine whether x and y are proportional. If x and y are proportional, fill in the blank with a number.
There is a population of 10,000 bacteria in a colony. If the number of bacteria doubles every 14 hours, what will the population be 28 hours from now?
Answer:
for the first 14 hours it doubles to 20,000, then once it reaches 28 hours it'll be 40,000. its an exponential growth
The population growth of bacteria after 28 hours will be equal to 40,000.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the set of information in the question,
Total population of Bacteria = 10,000
Rate of growth of bacteria = Twice in 14 hours
Rate of growth in 28 hours = 4 times the total population.
Then the total bacteria (B) in the colony after 28 hours,
B = 4 × 10,000
B = 40,000
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solve each system by substitution
-x+y=4
3x-2y=-3
Kallisto built a rectangular sign that measured 2 and 3/4. The width is 1 and 1/4 shorter than the length. To find the area, multiply the length and width. What is the area in square feet write an equation to solve it
Answer:
l = 1 5/16
w = 1/16
A = 21/16 x 1/16 = 21/256
Step-by-step explanation:
Perimeter = 11/4
l = length
w = l - 5/4
2l + 2(l - 5/4) = 11/4
2l + 2l - -5/2 = 1/4
multiply each side by 4
8l + 8l - 10 = 11
16l = 21
l = 21/16 or 1 5/16
width = 21/16 - 20/16 = 1/16
In a store, 9/200 of the shirts are pink and 69/600 are orange. What percent of the shirts are not pink or orange?
Answer:
84%
Step-by-step explanation:
The percentage of pink shirts
= 9/200 × 100%
= 9/2
= 4.5%
The percentage of orange shirts
= 69/600 × 100%
= 69/6
= 11.5%
The percentage of the shirts which are not pink or orange
= 1 - 4.5% - 11.5%
= 84%
Alternative
Find their common denominator.
9/200
= 9×3 / 200×3
= 27/600
The total percentage of shirts in pink and orange
= (27/600 + 69/600) × 100%
= 96/600 × 100%
= 16%
The percentage of the shirts which are not pink or orange
= 1 - 16%
= 84%
8. Stan made 4 goals out of 6 attempts in soccer today. What fraction
of attempts did Stan make? Please help
Answer:
[tex]\frac{4}{6}[/tex]
Step-by-step explanation:
URGENT!!! 20 points and Brainliest to best answer!
Complete the following proof.
Given: AB , CD are diameters
Prove: BD = CA
Answer:
angle AOC = BOD vertical angles
AO=BO bisected by CD
CO=DO biscted by BA
AOC =BOD SAS
Step-by-step explanation:
: D
Answer:
angle AOC = BOD vertical angles
AO=BO bisected by CD
CO=DO bisected by BA
AOC =BOD SAS
what is the value of X
Answer:
B) 24
Step-by-step explanation:
A right triangle is 90°
90-42=48
48/2=24
Answer:
24°
Step-by-step explanation:
We know that it's a right angle. First, subtract 42 from 90 (90° is a right angle)
90 - 42 = 48
Now, since there's a 2x on the other side, we need to divide 48 by 2 to get the value of x:
48 ÷ 2 = 24
Therefore, x = 24°
Investigators conducting a study regarding the effects of water pollution and peptic ulcer disease obtained the following data: A population of 9000 men and women, aged 45, were examined on January 1, 1985. Of these people, 6000 were exposed to toxins in the local water supply and 3000 were not. At the time of this exam, 90 cases of peptic ulcer disease were discovered; 60 of these cases were among those exposed to toxins in their local water. All the people at the initial exam who were free from peptic ulcer disease were followed with repeat exams over the following year. This study revealed 268 new cases in the total group; of these, 238 cases were among those exposed to toxins in their local water. A. Calculate the prevalence per 1000 people of peptic ulcer disease on January 1, 1986: Among the exposed Among the unexposed B. Calculate the 1985 incidence rate/1000 people of peptic ulcer disease: Among the exposed Among the non exposed
Answer:
Kindly check explanation
Step-by-step explanation:
The prevalence per 1000 among the exposed :
Total number of diseases among those exposed = 60 + 238 = 298
Prevalence per 1000 among the exposed :
(298 / 9000) * 1000 = 33.11
Prevalence per 1000 among the non exposed :
((90 - 60) + (268 - 238)) / 3000
(60 / 3000) * 1000 = 20
Incidence rate per 1000 among the exposed :
238 / 5940 * 1000
0.0400673 * 1000 = 40.07
Incidence rate per 1000 among the unexposed :
((90 - 30) / (3000-30)) * 1000
(60/2970) * 1000 = 20.2
what is the surface area, in centimeters, of a cube with a side length, s. of 1/3cm?
Jason represented the values of his 35 baseball cards in a histogram and in a stern-and-leaf plot. Which of these best describes the graph and characteristic that allow Jason to find the median value of his 35 baseball cards?
are there any choices?
Step-by-step explanation:
Find the value of x
Answer:
3
Step-by-step explanation:
bigger triangle is the special 5 12 13
so the hypotenuse is 13
the smallest side is 5
and the medium side is 12
sincd the sides of the smaller triangle are 4 and 5
x must be 3 because of 3 4 5 triangles
Use algebra to show that the recurring decimal 0.2813 =
557
198
Step-by-step explanation:
tell me the answer when u get too!!
btw its 557/1980
The proof is shown in the solution.
What are recurring decimals?A repeating decimal or recurring decimal is a decimal representation of a number whose digits are periodic, and the infinitely repeated portion is not zero.
Given that, show that the recurring decimal 0.2813 = 557 / 198
Let 0.2813 be x
0.2813 = x......(i)
2813.2813 = 10000x......(ii)
Subtracting eq(i) from eq(ii)
2813 = 999x
x = 2813 / 999
x = 557 / 198
Hence, proved
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Suppose that when your friend was born, your friends parents deposited $2000 in an account paying 5.9% interest. What will the account balance be after 15 years?
Answer:
FV= $4,725.74
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $2,000
Number of periods (n)= 15 years
Interest rate (i)= 5.9% = 0.059
To calculate the Future Value, we need to use the following formula:
FV= PV*(1 + i)^n
FV= 2,000*(1.059^15)
FV= $4,725.74
which lengths could represent the side lengths of a right triangle
suppose g(x)=f(x+1)+5.which statement best compares the graph of g(x) with the graph of f(x)
Answer:
g(x) : horizontal transformation to the left 1 unit and vertical transformation UP 5 units to f(x)
Step-by-step explanation:
g(x) : horizontal transformation to the left 1 unit and vertical transformation UP 5 units to f(x)
What is the value of the y-coordinate of point A
Answer:
there's no pic
Step-by-step explanation:
can you re attach it plz I might be able to help
PLEASE HELP, IT WOULD BE GREAT IF SOMEONE COULD ANSWER QUICKLY AND CORRECTLY!!!!
DONT LINK ANY FILES!!!
Which expression represents the perimeter of the figure below?
Answer:
5x+2y+z
Step-by-step explanation:
just count all of the variables
Answer:
C
Step-by-step explanation:
10 ft
5 ft
2 ft
Find area!!!
Answer:
Step-by-step explanation:
Volume = Length x width x height
length (10)
width (2)
height (5)
10 x 2 x 5 = 100
Area = Length x width
10 x 2 = 20ft
A polr has a shadow that is 15 feet long.Mary is 4 feet tall and her shadows is 10 feet tall how tall is the pile
Answer:
The pole is 6 feet tall.
Step-by-step explanation:
The height makes the perpendicular and the shadow makes the base of the triangle in the given question
Pole Mary
Height x 4
Shadows 15 10
If the height is taken along y- axis and shadow is taken along x axis
Then
tan alpha = Perpendicular/ base
for Mary Tan alpha = 4/10
For the pole = tan alpha = x/15
Comparing x/15= 4/10
x= 4*15/10= 60/10= 6
The pole is 6 feet tall.
Probability of getting 2 hears and 1 diamond in the first draw of 52 cards
Answer: 26/52
Step-by-step explanation:
Find the area of rectangles with the following dimensions.
a. 2 ¼ yd × ¼ yd =
b. 2 ½ ft × 1 ¼ ft = _____
Answer:
I think this is the answer I hope I have helped you
Step-by-step explanation:
a
b
Evaluate:
1/2×2.4×2.4×7=
Answer:
20.16
Step-by-step explanation:
hope it helps!!:)
help needed! no links please, they're annoying.
Pete bought a house in 2009 for $200,000.
The value of his house increased by 10%
annually.
Answer:
Value of house in 2021 = $627,680 (Approx.)
Step-by-step explanation:
Given:
Value of house in 2009 = $200,000
Rate increased per year = 10% annually
Find;
Value of house in 2021
Computation:
Number of year = 2021-2009 = 12 year
Value of house in 2021 = Value of house in 2009[1+Rate increased per year]ⁿ
Value of house in 2021 = 200,000[1+10%]¹²
Value of house in 2021 = 200,000[1+0.1]¹²
Value of house in 2021 = 200,000[1.1]¹²
Value of house in 2021 = 200,000[3.1384]
Value of house in 2021 = $627,680 (Approx.)
A cylinder has a diameter of 14 cm and a volume of 112 pi.
What is the height in, centimeters, of the cylinder?
(PS I am literally giving 15 points for the correct answer!!!)
HELP! :(