In mathematical terms, the equation e^-2.5 = h states that the exponential value of -2.5 (e^-2.5) is equal to the variable h. To convert this equation into its logarithmic form, we can take the natural logarithm of both sides of the equation. The natural logarithm, represented by the function ln, returns the power to which e must be raised to obtain a given number.
So, taking the natural logarithm of both sides of the equation, we have:
ln(e^-2.5) = ln(h)
Since ln(e^x) = x, we can simplify the left side of the equation:
ln(h) = -2.5
Thus, the logarithmic equivalent of the equation e^-2.5 = h is ln(h) = -2.5.
The logarithmic equation ln(h) = -2.5 can be interpreted as follows: the natural logarithm of h is equal to -2.5. In other words, h is the result of raising e to the power of -2.5. To find the value of h, we can use the exponential function:
h = e^-2.5
Therefore, the original equation e^-2.5 = h and the logarithmic equation ln(h) = -2.5 are mathematically equivalent and can be used interchangeably.
It is worth mentioning that logarithms are used in many areas of mathematics and science, including engineering, finance, and physics. They allow us to simplify complex calculations and to solve problems that are otherwise difficult or impossible to solve.
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y=x^2+4x+3? using a table of values-3 to3
The required graph of the function y=x²+4x+3 for the interval -3 ≤ x ≤ 3.
What is the graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
The given function,
y=x²+4x+3
Since we have given the interval for the value of the x, as -3 to 3
By putting value in the above expression we get y,
put x = -3
y = (-3)² + 4(-3) + 3
y = 9 - 12 + 3
y = 0
Similarly, other values are shown through the map.
Thus, the required graph of the function y=x²+4x+3 for the interval -3 ≤ x ≤ 3.
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Please help, I am trying to get this question answered.
The given triangles OML and ONP are similar triangles by SAS postulate.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
Here,
Consider triangle OML and ONP
OL / OP = OM/ON
13.5/3 = 9/2
4.5 = 4.5
And
∠O = ∠O [common angle]
Thus, both triangles are similar triangle by the SA postulate of similarities.
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Solve |5x – 1| = |2x + 5| Question 12 options: A) x = 1∕2 B) No solutions C) x = 2 or x = –4∕7 D) x = –1∕2 or x = –7
Answer: C) x=2 or x=-4/7
Please help me with this question.
For a, the percentage of given angle with respect to whole rotation is 0.36% and 1.3° is equivalent to 0.0072π radian.
What is the percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.
Examples of percentages are:
10% is equal to 1/10 fraction.
20% is equivalent to ⅕ fraction.
25% is equivalent to ¼ fraction.
Now,
Given angle=1.3°
Total rotation = 360°
So, percentage of given angle=1.3/360*100=0.36%
and 1.3° in radian=1.3*π/180=0.0072π
Hence,
the percentage of given angle with respect to whole rotation is 0.36% and 1.3° is equivalent to 0.0072π radian.
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In a rectangle ABCD, P is any point on side AB such that ∠BPC = ∠ADP, AP = 6 cm, BC = 8 cm, PD = 10 cm, then find the length of PC.
1. 13.33 cm
2. 12.5
3. 6 cm
4. 7.5 cm
The correct answer is option 1. 13.33 cm. In a rectangle ABCD, The length of PC is 13.33 cms.
In a right triangle BPC, we have two sides: BP = AP = 6 cm and PD = 10 cm. Using the Pythagorean theorem, we can find the length of PC:
[tex]PC^2 = BP^2 + PD^2\\= > PC^2 = 6^2 + 10^2\\= > PC^2 = 36 + 100\\= > PC^2 = 136\\= > PC = \sqrt{136} \\= > PC = 13.33 cm[/tex]
In the rectangle ABCD, we have a right triangle BPC. Point P is on side AB and is such that ∠BPC = ∠ADP. Therefore, BP and PD are the corresponding sides of the two right triangles. Using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (PC) is equal to the sum of the squares of the lengths of the other two sides (BP and PD), we can find the length of PC.
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Together, teammates Pedro and Ricky got 2681 base hits last season.Pedro had 285 more hits than Ricky. How many hits did each player have?
Using concept of linear equation, Pedro hit runs=1483 and Ricky hit runs=1198.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Given,
Together, teammates Pedro and Ricky got 2681 base hits last season. i.e. P+R=2681 -->1 where P=Pedro and R=Ricky
Pedro had 285 more hits than Ricky i.e. P-R=285 --->2
Solving equation 1 and 2 we get
P=1483 and R=1198
hence,
Pedro hit runs=1483 and Ricky hit runs=1198.
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Choose the measurement closest to 150 cm: 5 ft, 150 in. or 380 in.
To save for retirement, starting from her 30th birthday (t = 0), Miss Saver will invest
some money each year in a 30-year deposit in her bank saving account. The first
payment of $1000 will be made at the beginning of the first year. Every subsequent
payment increases by 5%.
She will retire at age 60, and will withdraw $X each year from her bank saving account
from then. The first withdrawal will be made at age 60. After 20 years (i.e. after the
20th withdrawal), she will have taken out all the money she had saved.
Assuming the effective annual interest rate is 2% perpetually, compute the value of X.
Give your answer to the nearest integer.
Miss Saver needs to withdraw $391 each year from her bank.
How to determine the value of XTo solve this problem, we need to
calculate the future value of the savings account at age 60,Then determine the annual withdrawal amount that will exhaust the account after 20 years.First, we need to determine the total amount of money Miss Saver will have saved using:
Total = $1000 * (1 + 0.05)^30 = 4321.94
Next, we need to determine the future value of this amount after 30 years at an effective annual interest rate of 2%.
This is done using
$4321.94 * (1 + 0.02)^30 = $7828.60
Now, we can determine the annual withdrawal amount, X as follows
X = $7828.59/20 = $391.4295
Rounding up to the nearest integer, X = $391
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Can someone please help me with this I need to figure out the formula
Answer:
j=19
Step-by-step explanation:
In the image, it shows that the weight of 5 + j is equal to the weight 24. Using this information, let's create a equation and solve for j:
5 + j = 24 [Subtract 5 from both sides]
j = 19
So, j must equal 19 for both sides of the hanger to be equal.
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After previewing and cleaning your data, you determine what variables are most relevant to your analysis. your main focus is on rating, cocoa.percent, and bean.type. you decide to use the select() function to create a new data frame with only these three variables.assume the first part of your code is: trimmed_flavors_df <- flavors_df %>% add the code chunk that lets you select the three variables.1
The correct answer is A, Canada. This is because the select() function allows you to specify the exact variables to be included in the data frame, and Company.Location is one of the variables that was specified in this case.
The first row of the table created using the select() function contains the data for the three selected variables from the original flavors_df data frame. The select() function was used to create a new data frame with only three variables: Rating, and Cocoa.Percent, and Company.Location. This function was used to filter out all the other variables from the original flavors_df data frame, leaving only the three variables of interest.
When looking at the first row of the table, the value in the Company.Location column is Canada, which is the country in the company producing the chocolate is located in.
Complete question:
After previewing and cleaning your data, you determine what variables are most relevant to your analysis. Your main focus is on Rating, Cocoa.Percent, and Company.Location. You decide to use the select() function to create a new data frame with only these three variables.
Assume the first part of your code is:
trimmed_flavors_df <- flavors_df %>%
Add the code chunk that lets you select the three variables.
select(Rating, Cocoa.Percent, Company.Location)
What company location appears in row 1 of your table?
Single Choice Question. Please Choose The Correct Option ✔
A. Canada
B. Scotland
C. France
D. Columbia
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descrive how determine f(x) and g(x) when x=
From the options given in the problem statement the values of f(x) and g(x) that satisfy equation (2) i.e. y = f(g(x)) = (10)/(√(2x + 9))are:f(x) = 10/√(x) and g(x) = 1/(2x + 9)
What is function ?
Function can be defined in which it relates an input to the output.
In this problem y is called a composite function of f(x) and g(x). So in the options given in the problem statement which option will satisfy y = f(g(x)) is to be found out.
Let f(x) be defined as some function then if ‘x’ is replaced by g(x) in f(x) i.e. f(g(x)) then its value will be y. Hence we can write:
y = f(g(x)) --- (1)
We are also given that
y = (10)/(√(2x + 9))
Let us consider each of the cases given under options, one by one. We have to find out the nature of the function f(x) as well as g(x) so that we substitute g(x) for x in f(x) we have:
y = (10)/(√(2x + 9))
(i) Consider f(x) = 10 and g(x) = √(2x + 9)
Here f(x) cannot take g(x) as its inputs.
(ii) Consider f(x) = 10/√(x) , g(x) = 2x + 9
Here we determine that f(g(x)) = (10)/(√(2x + 9))
(iii) Consider f(x) =10/x , g(x) = 2x + 9
Here f(g(x) = 10/(2x+9)
(iv) Consider f(x)= √(2x + 9) , g(x) = 10
f(g(x) = f(10) = √(2(10) + 9) = √29
Hence, From the options given in the problem statement the values of f(x) and g(x) that satisfy equation (2) i.e. y = f(g(x)) = (10)/(√(2x + 9))are:
f(x) = 10/√(x) and g(x) = 1/(2x + 9)
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a recycling bin contains 4 kg of glass and 500 g of plastic what is the ratio of glass to plastic in the bin?
Answer: 8:1
Step-by-step explanation:
Since there are 1000 grams in 1 kilogram, we can start by converting the 4 kg of glass to kilograms.
4 x 1000 = 4000, so this means that we have 4000 grams of glass in the bin.
So right now, the ratio of the glass in the bin to the plastic in the bin is 4000:500.
We can simplify: Start by dividing 100 from both numbers. Now, your ratio will look like this: 40:5. We can simplify even further, so divide 5 from both sides to get the ratio 8:1.
I hope this helps!
6 pounds more than twice the weight, w
2x+6 is the required weight.
The weight of an object is defined as the force acting on the object due to gravity. It is a scalar quantity. Weight is measured in newtons.
In Physics, the gravitational force with which the earth attracts all the masses to its center is called weight.
In the given question,
Let the weight of an object is x.
6 pounds more than twice the weight means the required weight of an object will be the 2×weight of the object(x) + 6 pounds.
Therefore,
2x+6 is the required weight of the object.
The complete question is,
The weight of 1st object is x. The weight of the second object is 6 pounds more than twice the weight. What is the weight of the second object?
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The needed weight is 2x+6.
The force exerted on an object by gravity is known as the weight of the object. It has a scalar value. Newtons are a unit of weight.
Weight is the term used in physics to describe the gravitational force that pulls all masses toward the center of the earth.
In the posed query,
Let's say that an object weighs x pounds.
The needed weight of an object is the weight of the object(x) plus 6 pounds, which is 6 pounds more than twice the weight.
Therefore,
The object must weigh at least 2x+6.
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The complete question is:-
The first item weighs x pounds. The second object weighs 6 pounds more than it does, or more than twice as much. What does the second object weigh?
Complete a piecewise defined function that describes the graph.
The piecewise function that defines the graph is given as follows:
y = x + 1, x < -2.y = -6, x = -2.y = 5, -2 < x ≤ 1.How to define the piecewise function?A piecewise function is a function that has different definitions, according to the input values assumed by the function.
The different definitions for the function in this problem are given as follows:
Left of -2: x < -2.x = -2.Left of x = -2 to x = 1: -2 < x ≤ 1.To the left of x = -2, the function is increasing with a slope 1, hence it would cross the y-axis at y = 1, and the definition is given as follows:
y = x + 1, x < -2.
At x = 2 and between x = -2 and x = 1, the function is constant.
Missing InformationThe piecewise function is given by the image presented at the end of the answer.
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select all That apply I’ll give you brainliest
Answer:
[A] The U.S has more people under 18 than China does.
[B] There are more people under 18 than age 45 to 64 in the U.S
[D] There are more people age 19 to 44 than any other age group in the U.S
Step-by-step explanation:
Based on the graph we know that:
Green = U.S
Dark Blue = China
Now let's look at our answer choices:
[A] The U.S has more people under 18 than China does.
Now looking at the graph we can see there are more green than dark blue which means U.S have more people under 18 than China does.
[B] There are more people under 18 than age 45 to 64 in the U.S
Based on the graph and estimate :
Under 18 in U.S = 25
Age 45-64 in U.S = 21 or 22 ish.
As we can see, there are more people under 18 than age 45-64 in the U.S
[C] The population of China is more than 4 times that of U.S
Graph don't really prove enough info to prove China population is more than 4 times of U.S.
But based on the graph, it doesn't look like population of China is more than 4 times that of U.S
[D] There are more people age 19 to 44 than any other age group in the U.S
Based on the graph we can see that out of all the age group - age 19 to 44 have the highest percentage which mean there are more people age 19-44 than any other age group in the U.S
RevyBreeze
please answer
i need help
Step-by-step explanation:
The equation being
D = -65m
They provides us with m
We can plug it in to find out the value of D
The first one is 0
D = -65(0) = 0m
The second is 1
D = -65(1) = -65m
And the last one is 2
D = -65(2) = -130m
Please help answer this !!!!
Answer:
Below
Step-by-step explanation:
L x H = area
(x+5) (x-2) = x^2 +3x -10 cm^2
Answer:
Answer is c
Step-by-step explanation:
IREADY AREA please help me due now thank uu!
According to the information, it can be inferred that the words that complete the sentences are: Radius, 3.14, radius, circumference, and both.
How to complete the sentences?To complete the sentences we must read each of them several times and identify its main theme; this will help us identify the missing term by context.
Additionally, we must read the text on the left side where we will find related information that will help us find the correct terms.
According to the above, the complete sentences would look like this:
In Rachel's method, 4 represents the radius of the rug, and the fraction 11/7 3.14 a good approximation for
In Erik's method, the height of the parallelogram is approximately equal to radius and the length is approximately equal to circumference.
Therefore, both suggested a reasonable method for approximating the area of the rug.
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How much do u study? A survey among freshmen at a certain university revealed that the number of hours spent on studying the week before final exams was normally distributed with the mean 25 and standard deviation 7. Between what two values are the middle 80% of the hours spent studying?
On solving the provided question, we can say that so, standard deviation ,we have 2nd > DISTR> Vars> (-10000;37;25;4)
What is standard deviation?Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed.
[tex]X = N(25,4)\\u = 25, z = 4\\P(X > 35)\\P(X < 35) = P( Z > 35 - 25/ 4) = P(Z > 2.5)\\2nd > DISTR > Vars > normalcdfnormalcdf(-10000;37;25;4)[/tex]
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Describe and correct the error in solving the exponential equation.
(will mark brainliest!)
Answer:
second step
Step-by-step explanation:
1/8 is not equal to 2^3 but instead it is equal to 2^-3
Use law of sines and show all work please!!
Answer:
[tex]C = 16.8954 ^\circ[/tex]
Step-by-step explanation:
Law of Sines
The rule of sines states: If a, b, and c are, respectively, the lengths of a triangle's legs on either side of angles A, B, and C:
[tex]\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]
Given:
Side c = 13angle B = 28Side b = 21[tex]C = \sin^{-1} \left[ \dfrac {c \sin B}{b}\right][/tex]
[tex]= \sin^{-1}\left[\frac {{13}{\sin}(28 ^\circ)} {21}\right][/tex]
[tex]= 16.8954 ^\circ[/tex]
Thanks.
Find all the solutions to the equation: a) z^8 =1
b) z^5 + j2^5 =0
Particulary for question c), the solutions should be arranged in the order of magnitude of the phases i.e phases in increasing order. c) z^6−16z^3 +128 = 0
To solve the previous exercise step by step, we first need to break down the equation into its components:
z^6−16z^3 +128 = 0
Now, we can use the quadratic formula to solve this equation:
x = (-b ± √(b² - 4ac)) / 2a
In this case, we have:
a = 1 b = -16 c = 128
So, the quadratic formula reduces to:
x = (-(-16) ± √((-16)² - 4(1)(128))) / 2(1)
Simplifying, we get:
x = (16 ± √(256 - 512)) / 2
And finally we get the solutions:
x = (16 ± √(-256)) / 2
Which simplifies to:
x = (16 ± 4i) / 2
And the solutions are:
z = 2, 4i, -2, -4i
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I NEED THE ANSWER ASAP
If you were to write the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2--what would be the value of b?
y=mx+b
y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We have to find the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2
m=-2
Now let us find the y intercept
-3=-2(4)+b
-3=-8+b
-3+8=b
5=b
Hence, y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.
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A cable repair person has 7.6 meters of wire. Suppose each meter of the wire weighs 3.2 ounces. what is the weight of the wire.
The total weight of the wire is 24.32 ounces.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
Total length of the wire = 7.6 meters
Weight of each meter of wire = 3.2 ounces
Total weight of the wire = Total meter of the wire × Weight of each meter
= 7.6 meters × 3.2 ounces
= 24.32 ounces
Hence the weight of the total length of the wire is 24.32 ounces.
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You are buying a car worth $38,890.00 In 5 years. Suppose you will invest your money in a plan that pays 10.2% interest for 5 years, compounded monthly. How much should you invest?
For a car worth $38,890.00 a person should invest $23,403.660 for a rate of 10.2% for 5 years if compounded monthly.
What is Compound Interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
The amount is A = $38,890.00
The time period in years is t = 5 years
The rate is given as r = 10.2%
The amount is compounded monthly, so n = 12.
First, convert R as a percent to r as a decimal -
r = R/100
r = 10.2/100
r = 0.102 rate per year,
The formula for compound interest is -
A = P(1 + r/n)^nt
Where,
A = amount
P = principal
r = rate of interest
n = number of times interest is compounded per year
t = time (in years)
Substitute the values into the equation -
A = P(1 + 0.102/12)^(12)(5)
38,890 = P(1 + 0.0085)^(60)
38,890 = P(1 + 0.0085)^(60)
38,890 = P(1.661705)
P = 38,890 / 1.661705
P = 23,403.660
Therefore, the principal value is $23,403.660.
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6. At the football game they sold $3 hot dogs
and $2 sodas, which made the school $300. The
number of sodas sold was 10 more than two
times the number of hot dogs sold. Determine the
number of hot dogs and sodas sold.
Using algebraic equation, the number of hot dogs sold is 40 and the number of sodas sold is 90.
what is algebraic equation?algebraic equation, statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.
Given that they sold one hot dogs at $3 and one sodas at $2.
The number of sodas sold was 10 more than two times the number of hot dogs sold.
Let the number of hot dogs sold is x
The number of sodas sold is 2x + 10
The school made total $300. SO that,
x*$3 + (2x+10)*$2 = $300
⇒ 3x + 4x + 20 = 300
⇒ 7x + 20 = 300
subtracting 20 from both side of equation
⇒ 7x = 300 - 20
⇒ 7x = 280
divided both side by 7
⇒ x = 280/7
⇒ x = 40
so the number of hot dogs sold is 40.
and the number of sodas sold is 2x + 10
= 2*40 + 10
= 80 + 10
= 90
The number of sodas sold is 90.
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What is the value of this expression? 6+23×4−81‾‾‾√ =
Answer:
129
Step-by-step explanation:
6+23×4-√81 =6+132-9= 129
MCR3U0 Name: e) Sketch the function 8(x) and state the domain and range of the transformed function g(x). Important: On the same grid, use step-by-step transformations to arrive at the required new function. Use a different colour for each step and include a legend stating the equa tion of each new graph. The transformations should be shown in the following order. 1. Base Graph 2. Vertical reflection/stretch/compression (if any). 3. Horizontal reflection/stretch/compression (if any). st 4 Horizontal and Vertical translations (if any).
Answer:
The function 8(x) is a parabola that opens downward and is centered at (0,0). The domain of 8(x) is x∈R and the range of 8(x) is y∈[0,∞).
To arrive at the new function g(x), follow these steps:
Base Graph: The base graph of 8(x) is shown below.
Vertical Reflection: To reflect the parabola about the x-axis, multiply the function by -1. The new function is g(x) = -8(x).
Horizontal Reflection: To reflect the parabola about the y-axis, multiply the function by -1. The new function is now g(x) = 8(-x).
Horizontal and Vertical Translations: To translate the parabola 4 units to the left and 2 units up, add 4 to the x-coordinates and subtract 2 from the y-coordinates. The new function is g(x) = 8(x-4)-2.
The resulting graph is shown below. The domain of g(x) is x∈R and the range of g(x) is y∈[-2,∞).
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HELP PLS
14.2=2(-5.8+t)
Answer: t= 12.9
Step-by-step explanation:
14.2=-11.6+2t
25.8=2t
t=12.9
Q11 This table shows how much a garage pays its staff. Pay rates Working day Monday to Friday Saturday or Sunday Rate Normal rate 1/4 x normal rate 14=¾ Last week, a mechanic worked 7½ hours each day from Monday to Saturday. She did not work on Sunday. Her normal rate of pay is £10.80 an hour. Work out her total pay for last week. Show all your working
Her total pay for last week is given as follows:
£506.25.
How to obtain the total pay?The total pay is obtained applying the proportions in the context of this problem.
The rates are given as follows:
Monday to Friday -> normal rate of 10.80 euros an hour.Saturday -> 1.25 x normal rate = 13.50 euros per hour.The number of hours is given as follows:
7.5 hours each day from Monday to Friday.7.5 hours on Saturday.Hence the total earnings are given as follows:
5 x 7.5 x 10.8 + 7.5 x 13.50 = £506.25.
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