Answer:
The sum of the two numbers is 12.5
Step-by-step explanation:
First we write a system of equations.
One number is 4 times larger than the other.
y = 4x
The sum of their reciprocals is 1/2
1/x + 1/y = 1/2
Substitute
1/x + 1/4x = 1/2
1 + 1/4 = 1/2x
x = 2.5
Solve for other number
y = 4(2.5)
y = 10
The inverse of x is 2/5 or 4/10, and the inverse of y is 1/10. When added the sum is 5/10 or 1/2.
A teacher has a salary of $25,920 for her second year on the job. If this is 4.2% more than her first year salary, how much did she earn her first-year?
Answer:
i don't know the answer!!
I WILL GIVE BRAINLIEST Juan writes 3^2 ∙9^4 = 27^6 and the teacher marked it wrong. Explain Juan’s error.
Juan multiplied the bases together, and added the power together, therefore, his solution is wrong.
What is power?Power is the result of multiplying same number for n number of times. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.
The correct solution,
3² ∙ 9⁴
= 3² ∙ (3²)⁴
= 3² ∙ 3⁸
= 3¹⁰
Hence, Juan multiplied the bases together, and added the power together, therefore, his solution is wrong.
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12 ÷ 3 × (15 - 6) + 3
Answer:
39
Step-by-step explanation:
[tex]{ \blue{ \mathfrak{39}}}[/tex]
Step-by-step explanation:
[tex]{ \red{ \tt{ \frac{12}{3} }}} \times ({ \green{ \tt{15 - 6}}}) + { \red{ \tt{3}}}[/tex]
[tex]{ \red{ \tt{4}}} \times { \green{ \tt{9}}} \: + \: { \red{ \tt{3}}}[/tex]
[tex]{ \red{ \tt{36}}} + { \red{ \tt{3}}}[/tex]
[tex] = { \purple{ \mathfrak{39}}}[/tex]
Information about five planets is shown in the table below.
Diameter (km)
4.88 × 10³
1.43 x 105
1.28 x 10¹
6.78 × 10³
1.21 x 105
Planet
Mercury
Jupiter
Earth
Mars
Saturn
Mass (kg)
3.3 x 1023
1.898 × 1027
5.97 x 1024
6.42 x 1023
5.68 × 1026
a) Write down the name of the planet with the greatest mass.
b) Work out the radius of Mercury giving your answer as an ordinary number.
Answer:
Mass is the property of a body that measure its inertia. It is taken as the measure of the amount of material it contains and have weight in gravitational field
Mass is also refers as the weight of an object. It is measured in grams (g) and kilograms (kg)
Radius of an object is defined as a straight line from the centre of a circular object to the circumference of the circular object
According to the data given of five planets
(a) The planet which has greatest mass is Mars that is 6.42 x 1023 kg
Radius of a given object can be calculated by dividing the diameter of the given object by 2.
(b) Radius of the mercury = Diameter given in kilometers / 2
= 4.88 × 10³ / 2
= 2.44 x 103 km
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Find two consecutive even integers such that 6 times the smaller integer is 36 more than 3 times the larger integer. Please Help me!
The integers are 14 and 16.
How to calculate the value?Let the integers be represented by x and x+2.
It was stated that the consecutive even integers such that 6 times the smaller integer is 36 more than 3 times the larger integer.
This will be:
6(x) = 3(x + 2) + 36
6x = 3x + 6 + 36
6x = 3x + 42
6x - 3x = 32
3x = 42
Divide
3x/3 = 42/3
x = 14.
The larger number will be:
= x + 2
= 14 + 2
= 16
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really need an explanation
Find the equation of the line which passes through (6,2) and is parallel to the line with equation 3y=5x+2
Answer:
3y = 5x - 24
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3y = 5x + 2 ( divide through by 3 )
y = [tex]\frac{5}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{5}{3}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{5}{3}[/tex] x + c ← is the partial equation of the parallel line
to find c substitute (6, 2 ) into the partial equation
2 = 10 + c ⇒ c = 2 - 10 = - 8
y = [tex]\frac{5}{3}[/tex] x - 8 ← equation in slope- intercept form
multiply through by 3 to clear the fraction
3y = 5x - 24 ← equation of parallel line
Given f(x) = 5x squared of 2 + 2 and g(x) = 8 - 3x, find the following.
12. Find g[f(-2)].
11. Find flg(x)).
перший завод виготовляє 6000 деталей з них 2% бракованих а в другого 6% бракованих скільки деталей робить другий завод якщо разом в них 3%
Answer:
18000
Step-by-step explanation:
18 000, тому що якщо ви заробляєте 6 000 і маєте 2% дефектних деталей, помножте на 3, щоб отримати 6% дефектних деталей, які дають вам 18 000
Can someone tell me what 17-6+2 is please?
Answer:
[tex]\frac{3}{x-1}+\frac{2}{x+1}=\frac{5}{x}[/tex]
If point A (–1, 0) is the midpoint of segment CT, and T is located at (1, 2), what are the coordinates of point C?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad T(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +x}{2}~~~ ,~~~ \cfrac{ 2 +y}{2} \right) ~~ = ~~ \stackrel{\textit{\LARGE A}}{(-1~~,~~0)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1+x}{2}=-1\implies 1+x=-2\implies \boxed{x=-3} \\\\\\ \cfrac{2+y}{2}=0\implies 2+y=0\implies \boxed{y=-2}[/tex]
Can somebody please help me?
Please help!! Questions 16-19
Answer: 16. f(1)=-2
17. f(-3)=1
18. x=0
19. x=-1 and x=1
Step-by-step explanation:
16. f(1)=-2
17. f(-3)=1
18. f(x)=-3
x=0 ==> f(0)=-3
19. f(x)=-2
x=-1 and x=1 ==> f(-1)=-2, f(1)=-2
if the length of a rectangle is increased by 30 percentage and the width of the same rectangle is decreased by 30 what is the affect on the area
Answer:
The area will decrease by 9%.
Step-by-step explanation:
The area of a rectange is given by the formula below.
[tex]\boxed{\text{Area of rectangle}= \text{length}×\text{width}}[/tex]
Let the original length and width of the rectangle be L and W respectively.
Start by finding the original area:
Original dimensions
Length= L= 100%L
Width= W= 100%W
Original area= LW
Let's find the dimensions of the new rectangle in terms of L and W.
New dimensions
Length= (100% +30%)L= 130%L
Width= (100%-30%)W= 70%W
New area
[tex] = \frac{130}{100} L \times \frac{70}{100} W[/tex]
[tex] = \frac{91}{100} LW[/tex]
= 91% LW
Comparing the new area with the original area:
100% LW- 91% LW= 9% LW
∴ The area will decrease by 9%.
*Note that percentage is equivalent to dividing a number by 100.
how do you find the y-intercept from vertex form
It is found that the intercepts can be found from vertex form, if the graph is hovering above the x axis (k<0).
What is y-intercept of a function?The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.
Assume that we've got: y = f(x) At y-axis, we've got x = 0, so putting it will give us the y-intercept. Thus, y-intercept of y = f(x) is y = f(0)
If a quadratic equation is written in the form y=a(x-h)² + k
therefore it is called to be in vertex form. It is called so because when you plot this equation's graph, we will see vertex point(peak point) is on (h,k)
To convert the given equation to vertex form, We will take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.
To find the intercepts, if the graph is hovering above the x axis (k<0) then there will be no real solutions for the x intercept.
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Help please!
The area of a square is 9 square feet. What is the length of one side of the square?
Answer:
the length of one side of square is 3
among cbc students, 50% of students are enrolled in less than three courses and 33% of students are taking a math class. if 71% of students are either enrolled in less than three courses or taking a math course, what percentage of students are enrolled in less than three courses and taking a math course? group of answer choices 38% 35.5% 17% 83% 12%
12% of students are enrolled in less than three courses and taking a math course
For given question,
50% of students are enrolled in less than three courses and 33% of students are taking a math class.
The probability that the students are enrolled in less than three courses is 0.5
P(A) = 0.5
The probability that the students are taking a math class is 0.33
P(B) = 0.33
if 71% of students are either enrolled in less than three courses or taking a math course.
P(A ∪ B) = 0.71
We need to find the percentage of students that are enrolled in less than three courses and taking a math course.
i.e., we need to find P(A ∩ B)
We know that, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∩ B) = 0.5 + 0.33 - 0.71
P(A ∩ B) = 0.12
So, 12% of students are enrolled in less than three courses and taking a math course.
Therefore, 12% of students are enrolled in less than three courses and taking a math course.
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Which statements are true about the graph of the system of linear inequalities? Select two options.
y > 3x – 4
y < One-halfx + 1
The graph of y > 3x − 4 has shading above a dashed line.
The graph of y < One-halfx + 1 has shading below a dashed line.
The graphs of the inequalities will intersect.
There are no solutions to the system.
The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).
The statements that are true about the graph of the system of linear inequalities include:
The graph of y > 3x − 4 has shading above a dashed line.
The graphs of the inequalities will intersect.
How to illustrate the information?y means the shading will be above the corresponding line.
y means the shading will be below the corresponding line.
Together, the two graphs intersect the entire y-axis. Jointly, they only intersect the y-axis on the interval -4 < y < 1.
Therefore, the graph of y > 3x − 4 has shading above a dashed line and thee graphs of the inequalities will intersect.
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Answer:
A, C
Step-by-step explanation:
Which statements are true about the graph of the system of linear inequalities? Select two options.
y > 3x – 4
y < One-halfx + 1
The graph of y > 3x − 4 has shading above a dashed line.
The graph of y < One-halfx + 1 has shading below a dashed line.
The graphs of the inequalities will intersect.
There are no solutions to the system.
The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).
Edge 2022
Frozen hamburgers are sold in packages of 4 and hamburger buns are sold in packages of 6. What is the smallest number of hamburgers and buns that can be sold so the number of hamburgers equals the number of hamburger buns?
PLS ANSWER QUICK!!!!
Answer:
The least common multiple of 8 and 6
burgers: 6, 12, 18, 24
buns: 8, 16, 24
You make 24 burgers which is 4 packages
of meat patties and 3 packs of buns.
what numbers are missing from the pattern? 11,22,?,?,?,?,77,88,99
Please Answer ASAP!!! HURRY:)
Answer:
so it goes 11,22,33,44,55,66,77,88,99!
Step-by-step explanation:
Not that hard you're welcome kings and queens have a nice day
Maria purchased 1,000 shares of stock for $35.50 per share in 2003.
share. Express her capital gain
She sold them in 2007 for $55.10 per
as a percent, rounded to the nearest tenth of a percent.
Maria's capital gain is 55.2%.
Here, we are given that Maria purchased 1,000 shares of stock for $35.50 per share in 2003.
Thus, the total cost price of these shares = 1000 × 35.5
= $35500
In 2007, she sold all of the stocks for $55.10 per share
Thus, the total selling price of these shares = 1000 × 55.1
= $55100
Now, absolute gain = selling price - cost price
Here, Maria's absolute gain will be-
= 55100 - 35500
= 19600
Now, her percentage gain will be given by-
Gain % = absolute gain/ initial value × 100
= 19600/35500 × 100
= 55.2
Thus, Maria's capital gain is 55.2%.
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4. Which of the following is the same figure as EG?
a) EF
b) EG
c) EF
d) EG
- Which of the following is the same figure as DF?
a) GF
b)FD
c) DF
d) DE
6. Which of the following is the same figure as DG?
a) DG
b) EG
c)GD
d) EG
7. Which of the following is true about the figu
a) DE EF
b) ED=FG
c) EF FG
d) DF DE
Answer:
a) EF
c) DF
a) DG
a) DE EF
Step-by-step explanation:
. Two angles in a triangle have measures 30° and 57°. What is the measure of the
third angle?
Answer:
93
Step-by-step explanation:
first you add 30 and 57
where you will get 87
then subtract 87 from 180 and get 93
f(a) = a + 3. Find f(7)
Answer: a=1/2=0.5
Step-by-step explanation:
7(a)=a+3
Subtract a from both sides.
7a−a=3
Combine 7a and −a to get 6a.
6a=3
Divide both sides by 6.
a= 63
Reduce the fraction
63
to lowest terms by extracting and canceling out 3.
a= 21
is 5 1/25 irrational
a survey indicated that the vast majority of college students own their own personal computers what information would you want to know before you accepted the results of this survye
The required information is (B), (C), (D), and (I).
What is a survey?A survey in human subjects research is a set of questions designed to elicit specific information from a specific group of people. Surveys can be conducted over the phone, by mail, on the internet, or even on street corners or in shopping malls. In fields such as social research and demography, surveys are used to gather or gain knowledge.Survey research is frequently used to assess people's thoughts, opinions, and feelings.So,
A. Who paid for the survey? It is not required.
B. Who made up the population from which the sample was drawn? Needed.
We need to know if the sample is representative of the "college students" population, on which we are basing our conclusions.
C. What sampling strategy was used? Needed.
We want to know if the sample was chosen at random.
D. How large was the sample size? Needed.
This information is required to determine the accuracy of the results.
E. What are the colleges represented in the sample?
It's not necessary if we already know "B."
F. How many survey questions were there? It is not required.
G. How many people participated in the survey? It is not required.
H. What were the questions? It is not required.
I. Is the language in the questions clear, accurate, unbiased, and valid? Needed.
We want to know if the answer was unbiased and clear so that we can determine if the conclusions are also unbiased.
J. What day of the week was the survey held? It is not required.
Therefore, the required information is B, C, D, and I.
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The correct question is given below:
A survey indicates that the vast majority of college students own their own personal computers. What information would you want to know before you accepted the results of this survey? Select all that apply. A. Who funded the survey? B. What was the population from which the sample was selected? C. What sampling design was used? D. What was the sample size? E. What are the names of the colleges included in the sample? F. How many questions were asked in the survey? G. How many people conducted the survey? H. What questions were asked? I. Were the questions clear, accurate, unbiased, and valid? J. On what day of the week was the survey conducted? g
One week, Gabriel bought 2 bags of beans and 3 bags of rice. The next week, he bought 4 bags of beans and 1 bag of rice. Let b represent the cost of each bag of beans and r represent the cost of each bag of rice. Simplify the expression for the total cost, shown below.
(2b + 3r) + (4b+ r)
28 – 2.5x – 2y
32 + 2.5x + 2y
32 – 2.5x – 2y
:(
how to find the rise and run on the graph
rise: 1 run: 2
slope: 1/2
you can start from any point on the slope. if i picked point (-5,0) i go up 1 square and right 2 squares to get to point (-3, 0). thats basically the rise and run, and the slope is always rise over run
Expand and simplify (K+4)(7k+3)
Answer:
(k + 4) (7k + 3)
k(7k + 3) + 4(7k + 3)
7k² + 3k + 4(7k + 3)
7k² + 3k + 28k + 12
7k² + 3k + 28k + 12
7k² + 31k + 12
7k² + 31k + 12
Mr. Johnson earns $5.40 an hour. One week, he worked 40 hours and 2 hours overtime, If he is paid time and one-half for overtime, how much did he earn?
When Mr. Johnson earns $5.40 an hour. One week, he worked 40 hours and 2 hours overtime, If he is paid time and one-half for overtime then the total amount he earned is $232.2
Given,
The amount he earns in an hour = $5.40
Total number of hours he worked =40 hours
The amount he earns = 5.40×40 = $216
Overtime hours = 2 hours
Overtime payment per hour= 5.40×1.5= $8.1
The amount he earns for overtime = 2×8.1= $16.2
The total amount he earned = 216+16.2= $232.2
Hence, when Mr. Johnson earns $5.40 an hour. One week, he worked 40 hours and 2 hours overtime, If he is paid time and one-half for overtime then the total amount he earned is $232.2
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