The ratio of their shares is 1:2:3 and amount is 180.5, 3564, 5371.5 respectively.
To find the amount each received:
Atta received 13.5*(51+110) = 1807.5
Abena received 27*(51+110) = 3564
Kojo received 40.5*(51+110) = 5371.5
The total amount shared is 51 + 110 = 161
The ratio of their shares is 1:2:3, meaning Atta receives 1/6 of the total amount, Abena receives 2/6 of the total amount, and Kojo receives 3/6 of the total amount.
To find the amount each received, we multiply their respective share (1/6, 2/6, and 3/6) by the total amount (161)
Kojo received 3 times as much as Atta, and Atta received 1/2 times as much as Abena.
Atta received 1/6 of the total amount, which is (51 + 110)/6 = 81/6 = 13.5
Abena received 2/6 of the total amount, which is (51 + 110)*2/6 = 162/6 = 27
Kojo received 3/6 of the total amount, which is (51 + 110)*3/6 = 243/6 = 40.5
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Find the domain and the range of the relation shown on the graph to the right. Use the vertical line test to determine whether the graph is the graph of a function.
The domain and the range of the relation shown to the right are given as follows:
Domain: x >= -5.Range: All real values.The graph is not a function, as a vertical line for x > -5 would cross a function in multiple points.
How to obtain the domain and the range of the relation?The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, thus the domain is of:
x >= -5.
The range of a function is the set that contains all the output values of the function, hence on the graph it is the values of y, thus the domain is of:
All real values.
As there are inputs that are mapped to multiple outputs, the graph does not represent a function.
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A horse's body temperature T is considered to be normal if it is within at least 0. 9o F of 99. 9o F. Write the normal range of body temperature of a horse as an inequality
If horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F , then normal range of body temperature of a horse as an inequality 99 ≤ T ≤ 100.8 .
If the temperature of the horse denoted by "T" , is within at least 0.9 °F of 99.9 °F , then it is considered as Normal ;
To express this as an inequality, we can use the following:
⇒ 99.9 - 0.9 ≤ T ≤ 99.9 + 0.9 ;
Simplifying further , this inequality can also be written as:
⇒ 99 ≤ T ≤ 100.8
Therefore , the normal range of body temperature of a horse is 99 ≤ T ≤ 100.8 .
The given question is incomplete , the complete question is
A horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F. Write the normal range of body temperature of a horse as an inequality .
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HELP ME FIND M? WILL GIVE BRAINLIEST
Answer:
212
Step-by-step explanation:
277 - 68 ( I would give further explantion but it ez )
=
209
I’m so dum sorreh
Answer:
212
Step-by-step explanation:
277 - 65 =
212
an insurance company conducted an opinion poll for a new health policy. in a sample of 200 participants, 117 of them supported this policy. does this provide strong evidence that more than a half of americans are supporting the new health policy? find the -value of the test (round off to third decimal place).
Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.
What is null hypothesis ?
The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.
The null hypothesis is that the proportion of Americans supporting the new health policy is less than or equal to 0.5 (p <= 0.5). The alternative hypothesis is that the proportion of Americans supporting the new health policy is greater than 0.5 (p > 0.5).
The test statistic for a one-sample proportion test is:
z = (p^ - p) / sqrt((p * (1-p)) / n)
where p^ is the sample proportion (117/200 = 0.585), p is the hypothesized proportion of Americans supporting the new health policy (0.5), and n is the sample size (200).
Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.
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Meg is a veterinarian. She found that 10, or 33%, of the dogs she saw this week were boxers. Steve is also a veterinarian. He found that 50% of the 12 dogs he saw this week were boxers. Does each person need to find the part, the whole, or the percent?
What Meg needs to find is the whole and what Steve needs to find is the part.
How to solve Percentage problems?Suppose a number is 'a'
Suppose another number is 'b'
We want to know how much percent of 'b' is 'a'.
Then, it is calculated as:
a/b * 100
(in percentage)
Since Meg already knows the part and the percent which is 10 and 33% respectively, then it means that what she needs to find is the whole which is the total number of dogs she saw.
Steve already knows the whole which is 12 dogs and the percent which is 50% and as such what he will need to do now is to find the part that makes up the percentage part.
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Which are the roots of the quadratic function f(b) = b² - 75? Selec
Ob=5√3
Ob=-5√3
Ob=3√5
Ob=-3√5
Ob=25√3
The roots of the quadratic function f(b) = b² - 75 are Ob=5√3 and Ob=-5√3.
What is quadratic function?A quadratic function is a polynomial function of degree two, which means it is a function that can be expressed as an equation with the second-degree degree of the highest exponent of the unknown variable. It is typically expressed as ax^2 + bx + c, where a, b and c are constants, and x is an unknown variable. Quadratic functions can be used to model many real-world situations, such as the height of a projectile in motion or the area of a circle.
The Quadratic Formula can be used to solve for the roots of a quadratic function. The Quadratic Formula states that for a quadratic equation of the form ax² + bx + c = 0, the two roots are given by x = [-b ± √(b² - 4ac)]/2a.
In this case, a = 1, b = 0, and c = -75. Therefore, the two roots are given by x = [-0 ± √(0² - 4(1)(-75)]/2(1). This simplifies to x = [0 ± √(75)]/2, or x = ±5√3/2. The two roots are thus Ob=5√3 and Ob=-5√3.
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To avoid sharing his name with another famous Al, actor Albert Brooks changed his name from what? a. Al Pacino. b. Al Jolson. c. Albert Einstein.
d. Albert Schweitzer
Actor Albert Brook changed his surname to Albert Einstein to avoid sharing it with another well-known Al. Option C
In 1921, Albert Einstein received the Physics Nobel Prize in honor of his contributions to theoretical physics, particularly the creation of the law of the photoelectric effect. Despite moving to Switzerland in 1895 and giving up his German nationality the following year to become a citizen of the County of Württemberg, Einstein was born within the boundaries of the German Empire.
He enrolled in the program for teaching diplomas in physics and mathematics at the Swiss Federal University of Technology School in Zürich in 1897 as a 17-year-old, and he completed it in 1900.
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You invited 24 people to your house for a party. You want to spend a $70 gift card completely on the items shown. You also want to have exactly two servings of food for each person.
Pizza Chicken wings
$6.00 $7.00
4 servings 5 servings
Write a system of linear equations to model this situation where x represents the pizza and y represents the bags of wings.
How many pizzas should you buy? How many bags of chicken wings should you buy?
You have one additional guest that you forget to invite. Now, how many of each items should you buy so everyone still gets exactly two servings? Show or explain your work.
The amount of each item, pizza and chicken wings that should be bought are 7 and 4 respectively. For an additional member the additional number of pizzas is 0 and chicken wings are 10.
What is an equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
A: X is the quantity of pizzas, while Y is the quantity of bags of chicken wings.
1 pizza cost x, thus 6 cost = 6 x
1 bag of chicken wings costs y dollars, thus 7 cost = 7 y.
Given: Total cost = 6x + 7y = 70
Total servings are now equal to (24)(2) for a total of 48.
One pizza includes four portions, thus 1 x 4 = 4
Servings in a bag of chicken wings are 5y.
Servings total: 4x + 5y = 48
The set of linear equations is hence 1.
6x + 7y = 70 .....(I)
4x + 5y = 48 ......(II)
Having solved (I) and (II), we obtain x = 7 and y = 4.
B:
One more guest brings the total to 25.
Total portions are therefore 4x + 5y = 2.25 = 50.
The total cost of 6x + 7y stays at 70.
The set of linear equations is hence 1.
6x + 7y = 70 .....(I)
4x + 5y = 50 ......(II)
We obtain x = 0 and y = 10 by solving for (I) and (II).
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kallie and jeie et up lemonade tand in their front yard thi morning. They old both regular (for 1.50) and trawberry (for $2). They old 12 more trawberry lemonade than regular. If they made a total of $45, how many of each did they ell?
Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.
Regular Lemonade: 9
Strawberry Lemonade: 21
Regular Lemonade:
Price of Regular Lemonade = 1.50
Total earnings from Regular Lemonade = 9 x 1.50 = 13.50
Strawberry Lemonade:
Price of Strawberry Lemonade = 2
Total earnings from Strawberry Lemonade = 45 - 13.50 = 31.50
Number of Strawberry Lemonade sold = 31.50 / 2 = 15.75
Number of Regular Lemonade sold = 15.75 - 12 = 3.75
Rounded to nearest whole number,
Number of Regular Lemonade sold = 4
Number of Strawberry Lemonade sold = 16
Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.
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please hurry!! ............................
Answer:
Answer in image
Step-by-step explanation:
Using the y-intercept, we can graph our first point at (0,5) the y-intercept. Then from there we can use the slope to continue to plot points. (This is a negative graph by the way based off of the slope -3/4).
-Hope this helped
A specialty shop procures several oil paintings for $450 apiece and offers them to customers for $900 each. What percentage is the mark-up?
Answer:
100%
Step-by-step explanation:
The mark-up percentage is the amount by which the cost price of a product is increased to arrive at the selling price. To calculate the mark-up percentage, you can use the formula:
Mark-up percentage = (selling price - cost price) / cost price x 100
In this case:
Cost price = $450
Selling price = $900
Mark-up percentage = ($900 - $450) / $450 x 100 = 100%
So the specialty shop has a mark-up of 100% on each painting.
It means that the shop is charging twice as much as the price they procured the paintings.
AC=A, C, equals Round your answer to the nearest hundredth. A right triangle A B C. Angle A C B is a right angle. Angle A B C is twenty-five degrees. Side A C is unknown. Side B C is five units.
The unknown side BC is 2.33 units.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
A right triangle ABC.
∠ACB is a right angle.
∠ABC is twenty-five degrees.
The side AC is unknown.
Side BC is five units.
Now,
AC = x
BC = 5 units
Tan 25° = AC/BC
Tan 25° = x/5
0.47 = x/5
x = 5 x 0.47
x = 2.33
Thus,
Side BC is 2.33 units.
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A statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade. She randomly selects 12 students for study and asks them to keep track of these problems completed during the course of the semester. At the end of the class, each student's total is recorded along with their final grade. Select all the statements that are true based on the scatter plot
The scatter plot for the randomly selects 12 students is illustrated below.
The term called scatter plot in math is defined as a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.
Here we have know that the statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade.
Here we know that the number of samples is 12.
And here we have each student's total is recorded along with their final grade.
Then the scatter plot for the following table of data is illustrated on the diagram.
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INTEGRALS EXERCISES PLEASEEE HELP ME I’LL GIVE U A CROWN
INTEGRALS MATH
The principles of integration were formulated independently by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, who thought of the area under a curve as an infinite sum of rectangles of infinitesimal width.
What is Crown integrals?A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). Double integrals are the integrals of a function of two variables over an area in R2 (the real-number plane).
The double integral of a positive function with two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function with one variable represents the area of the region between the graph of the function and the x-axis.
A multiple integral will produce hypervolumes of multidimensional data if there are more variables.
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Question content area top
Part 1
A 150-pound person uses 6.7 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 250 calories?
The number of miles that a person walks at this speed to use at least 250 calories will be 2.49 miles.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
A 150-pound person uses 6.7 calories per minute when walking at a speed of 4 mph. If the number of calories burnt is 250. Then the number of minutes the person is given as,
T = 250 / 6.7
T = 37.313 minutes
T = 0.62 hours
Then the distance is given as,
D = 4 x 0.62
D = 2.49 miles
The number of miles that a person walks at this speed to use at least 250 calories will be 2.49 miles.
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Write an equation in slope intercept form passing through the point (-10,1) and parallel to the line 10x+5y=15.
An equation in slope intercept form passing through the point (-10,1) and parallel to the line 10x+5y=15 is y=-2x+19.
How to get the slope intercept form of a straight line equation?If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
y = mx +c
To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.
Given;
Line is passing through the point (-10,1)
Parallel to the line 10x+5y=15.
So, the slope of the line is equal to the line parallel to it
Slope of given line
5y=-10x+15
y=-10x/5+15
m=-2
Equation; 1=-2x+c
c=-2*-10-1
c=19
Therefore, the equation will be y=-2x+19.
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A truck that can carry no more than 7300 lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 300 lb and each piano weighs 425 lb. Write
and graph an inequality to show how many refrigerators and how many planos the truck could carry. Will 11 refrigerators and 9 pianos overload the truck? Explain.
Let x be the number of refrigerators in the truck and y be the number of pianos in the truck. Write an inequality to show how many refrigerators and how many pianos the
truck could carry.
(Use integers or simplified fractions for any numbers in the inequality. Do not factor.)
The required inequality to show how many refrigerators and how many pianos the truck could carry is 300x + 425y ≤ 7300.
What is inequality?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.
According to question:We have,
A truck that can carry no more than 7300 lb is being used to transport refrigerators and upright pianos.
Let x be the number of refrigerators in the truck and y be the number of pianos in the truck.
Then
300x + 425y = 7300
At x = 11 and y = 9
300(11) + 425(9)
= 7125 ib
So, the truck will not overload.
Inequality will we
300x + 425y ≤ 7300
Thus, required inequality is 300x + 425y ≤ 7300.
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Five hundred (500) children participated in a field demonstration. Their heights averaged 110 cm with a standard deviation of 6 cm. If the heights are normally distributed, how many children have a height greater than 116?
For the given normally distributed data, the number of children have height greater than 116 is given by 79.
Using normally distribution we have,
Z = ( X - µ ) / σ
Here,
Mean 'µ' = 110
Standard deviation 'σ' = 6 cm
n = 500
Number of children with height greater than 116 cm
P (x > 116) = 1 - P (x < 116)
For,
P( X < 116 )
⇒ P[ (X - μ) / σ > (116 - 110)/ 6 )
⇒ P( Z < 6 / 6 )
⇒ P( Z < 1 )
Using the value from normal distribution table we have:
P (Z< 1) = 0.8413
⇒P (x > 116) = 1 - 0.8413
⇒P (x > 116) = 0.1587
Number of children with height greater than 116 is :
= 0.1587 × 500
= 79.35
= 79 ( approximately )
Therefore, the number of children have the height greater than 116 cm is equal to 79.
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a sample of 800 computer chips revealed that 60% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that more than 57% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.02 level to support the company's claim? state the null and alternative hypotheses for the above scenario.
Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.
The null hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is less than or equal to 57%. The alternative hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is greater than 57%.
To test this, you would use a one-sample proportion test. The test statistic is calculated using the sample proportion (60%) and the hypothesized proportion (57%) and the sample size (800).
You would then compare the calculated test statistic to the critical value from a z-table (using a two-tailed test and a 0.02 level of significance) to determine whether or not to reject the null hypothesis.
Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.
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how to graph y=5x
y=45-10x
By plotting the given points (0,0) , (1,10 ) for y=5x and the points for y=45-10x are (0,45) , (1,35) and (2,25) we get the required graph.
What is linear equation ?
Linear equation can be defined as the equation in which highest degree is one.
Given Equation,
y = 5x and y = 45 - 10x
So,
use the slope form is
y= mx+b , where m is slope and b is the y-intercept.
find the valued of m an b using the form y = mx+b
m = 10 and b=0
The slope of line is the value of m and y-intercept the value of b
slope = 10
y-intercept = (0,0)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding 2y values.
create a table for x and y values.
x y
0 0
1 10
and soon
Similarly for y = 45-10x
x y
0 45
1 35
2 25
and soon
And Hence plot the points in the graph.
Therefore, By plotting the given points (0,0) , (1,10 ) for y=5x and the points for y=45-10x are (0,45) , (1,35) and (2,25) we get the required graph.
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A student simplifies the expression correctly. 3x+10/2+4(x+3/2). Which could be the student's result?
The correct result for the expression 3x + 10/2 + 4(x + 3/2) is solved to be
x = -1 4/7How to to simplify the expressionThe math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as
the full meaning include
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
applying the sequence the problem is solved as follows
= 3x + 10/2 + 4(x + 3/2)
parenthesis
= 3x + 10/2 + 4x + 6
division
= 3x + 5 + 4x + 6
addition
= 3x + 4x + 6 + 5
= 7x + 11
solving for x
7x = -11
x = -11/7
x = -1 4/7
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Consider the scatter plot.
Select an answer from the drop-down menu to correctly complete the statement.
The scatter plot shows a
Choose...
association.
Scatter plot of 10 points. Generally, the points form an upside down U shape.
The scatter plot shows data points that do not follow a trend, thus it shows a: nonlinear association.
How to find a Non-linear Association?A nonlinear association is a relationship between two variables, whereby a change in one does not correspond to a change in another.
Thus, on a scatter plot showing a nonlinear association, the data points do not follow a trend line and are scattered, therefore, predictions cannot be made using the scatter plot.
Thus, the scatter plot that is given shows: nonlinear association.
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Select the equivalent expression. \left(3^2\cdot 5\right)^{3}=?(3 2 ⋅5) 3 =?
The simplified exponential expression for this problem is given as follows:
(3² x 5)³ = 3^6 x 5³.
How to simplify the expression?The exponential expression for this problem is defined as follows:
(3² x 5)³.
As we have a product applied to the exponent, the exponent can be applied to each factor of the exponent, as follows:
(3²)³ x 5³.
Applying the power of power rule, we have that:
(3²)³ = 3^(2 x 3) = 3^6.
Hence the simplified exponential expression for this problem is given as follows:
(3² x 5)³ = 3^6 x 5³.
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40 points, please be quick :] links or wrong answers will be reported
Which of the following expressions is equivalent to 6a/2a^2?
The equivalent expression of 6a/(2a²) is 3/a.
And none of the given option is correct.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given:
An expression,
6a/(2a²)
Simplifying,
6a/(2a²),
= 6a /(2a×a)
= 3/a is the equivalent expression.
Therefore, 3/a is the equivalent expression.
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Does this shape belong in a group of shapes that have more than one
perpendicular sides?
Use the drop-down menus to explain your answer.
Yes, this shape belong in a group of shapes that have more than one perpendicular sides because its sides meet at a right angle.
What are perpendicular lines?In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles) as shown in the image (see attachment) attached below.
However, it should be noted that it is not all intersecting lines that are perpendicular to each other because the lines may intersect at different angles other than 90 degrees (90°).
By critically observing the geometric shape, we can reasonably infer and logically deduce that it has more than one perpendicular sides.
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Which demonstrates the MOST effective word order for the following sentence?
All communities, no matter how diverse, have a number of needs that can be met by student
volunteers.
O All communities have a number of needs that can be met by student volunteer, no matter how diverse.
O No matter how diverse, communities have a number of needs that can be met by student volunteers.
O All communities have a number of needs, no matter how diverse, that can be met by student volunteers.
O Leave it as is.
A varied group of volunteers is frequently better able to function as a team since having a variety of viewpoints and personalities helps facilitate collaboration.
What is diversity in volunteering?Diversity in volunteering refers to both the individuals participating and the opportunities offered. Regardless of ethnicity, gender, religion, sexual orientation, or other characteristics, volunteering should be a process that welcomes participation from people with a variety of backgrounds and talents.
People can learn from one another as a result of diversity, which introduces new ideas and experiences. Better problem-solving results from incorporating many ideas and perspectives. Working in diverse teams fosters innovation and encourages dialogue. Our culture benefits from variety as well.
Any employee, regardless of gender, race, age, ethnicity, physical ability, sexual orientation, religion, or other characteristic, has the same rights and opportunities in a diverse workplace.
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Invest $10000 in a stock with 5% compounded monthly. How much will you have in 10 years?
If you invested $10000 in a stock with 5% compounded monthly you will have $16470 in 10 years.
What is Compound interest?Compound interest is simply interest that is earned over prior interest. You receive interest on the initial principal as well as the interest that builds up over time when you open a savings account that pays compound interest.
When you deposit funds into a savings account or other type of account, you will earn interest on the amount you deposited. For instance, after a year, if you deposited $1,000 in an account with 1% annual interest, you would have received $10 in interest.
Compound interest formula is
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Here,
P = $10000
r = 5%
n = 12
t = 10
A = to find
Lets solve,
[tex]$\text A = 10000(1 + \frac{0.05}{12})^{12\times 10}[/tex]
A = 16470
Thus, If you invested $10000 in a stock with 5% compounded monthly you will have $16470 in 10 years.
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need help on number 14, don’t understand part B
The number of customers when there are 576 towers will be 12.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
Based on the information, it should be noted that the number of phone is proportional to the number of customers
The constant of proportionality will be:
= 252 / 5.25
= 48
Therefore, the customers when there are 576 towers will be:
= 576 / 48
= 12
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What must you do to keep the equation x + 5 = 12 balanced?
Answer:
see below
Step-by-step explanation:
make x = 7
Answer:
Subtract 5 from both sides
x = 7
Step-by-step explanation:
x + 5 = 12 Subtract 5 from both sides
x + 5 - 5 = 12 - 5
x = 7
what is one task that you can have students do to help them develop the 1st standard for mathematical practice: make sense of problems and persevere in solving them?
Students who are proficient in math begin by defining a problem for themselves and searching for possible solutions.
They examine assumptions, limitations, connections, and objectives. Instead of just launching into a solution attempt, they formulate hypotheses regarding the structure and significance of the solution and outline a solution pathway. In order to get insight into the problem's solution, they take into account similar difficulties, try specific situations, and take the original problem in simpler forms. They track and assess their development, and if necessary, they alter their direction. A good puzzle not only involves more of the "real world" for a child than, instance, calculating the amount of paint required.
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