Write the expression ;
The quotient of seven and a number, added to ten.
Answer: (7/x) + 10
A quotient is a result you get after dividing two numbers, for example, 10 divided by 2 is 5. 5 is the quotient because it's the result of 10/2. Hence, the quotient of seven and a number is simply (7/x), x being any number. And that value is added to 10, leaving us with the expression (7/x) + 10.
help asap thanks yall so much
Answer:
a and c
Step-by-step explanation:
if you evaluate each one on either side of the equal sign you get the same number on both sides
For each graph below, state whether it represents a function.
Answer:
graphs 2 and 4 are functions
Step-by-step explanation:
To know if a graph represents a function, draw multiple vertical (straight up and down) lines through the graph. If any of the vertical lines crosses the graph 2 or more times, it is NOT a function.
what is the present value of $2525 per year, at a discount rate of 10 percent, if the first payment is received 9 years from now and the last payment is received 24 years from now?
The present value of $2525 per year, at a discount rate of 10 percent, if the first payment is received 9 years from now and the last payment is received 24 years from now is; $9215.77
What is the Present Value of Annuity?
An annuity is defined as a fixed amount of cash that is received or paid periodically over a certain period of time. This would mean that the amount in each cash flow of the annuity would be equal and occur for a specific period of time.
The formula for present value is;
PV = P[1 - (1 + r)⁻ⁿ)/r]
where;
PV is present value
P is periodic cash flow
r is interest rate
n is time
We are given the following;
Periodic cash flow (P) = $2525 /Year
Interest rate (r) = 10% /Year = 0.1
Time (n) = 16 Year (from 9 years to 24 years)
Thus;
PV = 2525[1 - (1 + 0.1)⁻¹⁶)/0.1]
PV = $19754.86
This is the present value in 9 years
Thus, the present value in 24 years which is now will be expressed by the formula;
PV = FV/(1 + i)^(t)
where;
PV is present value
FV is future value
i is interest rate
t is time
Thus;
PV = 19754.86/(1 + 0.1)^(8)
PV = $9215.77
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Using the declining-balance method, complete the table as shown (twice the straight-line rate): (Enter your answers as a whole dollar amount.)
Auto $29,000
5 years
Residual $2,000
Year Cost Accumulated
Depreciation B.O.Y Book Value B.O.Y Depreciation
Expense Accumulated
Depreciation E.O.Y Book Value E.O.Y
1 A B C D E F
2 G H I J K L
3 M N O P Q R
Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
What is the double-declining-balance method?The double-declining-balance method is one of the depreciation methods in use, but it allocates more cost to the earlier years of the asset's life.
This depreciation method uses twice the straight-line rate, which is computed as the product of 100/estimated useful life multiplied by 2.
For each year's depreciation expense, the double rate is applied at the end of the year's balance.
For the last year, the difference between the previous year's ending balance and the residual value is taken as the depreciation expense.
Auto = $29,000
Estimated useful life = 5 years
Residual = $2,000
Depreciable amount = $27,000 ($29,000 - $2,000)
Straight-line depreciation rate = 20% (100/5)
Double-declining depreciation rate = 40% (20% x 2)
Depreciation Expense:1st year = $11,600 ($29,000 x 40%)
2nd year = $6,960 ($17,400 x 40%)
3rd year = $4,176 ($10,440 x 40%)
4th year = $2,506 ($6,264 x 40%)
5th year = $1,758 ($3,758 - $2,000)
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
4 $29,000 $22,736 $6,264 $2,506 $25,242 $3,758
5 $29,000 $25,242 $3,758 $1,758 $27,000 $2,000
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Devontae claimed that the line y=-3/4x forms an angle of about 53.13° with the positive x-axis. Which statement proves his claim correct or incorrect?
a) Correct because arctan(4/-3) = -53.13
b) Correct because arccos(-3/4) = 53.13
c) Incorrect because arctan(-3/4) = -36.87
d) Incorrect because arccos(-3/4) = -138.59
The statement that proves the claim about the angle is incorrect is that;
c) Incorrect because arctan(-3/4) = -36.87
How to solve Trigonometric Ratios?The 6 main trigonometric ratios of a right angle triangle are;
Sine θ = length of the opposite leg / length of the hypotenuse
Cosine θ = length of the adjacent leg / length of the hypotenuse
Tangent θ = sine θ/cosine θ = opposite leg / adjacent leg.
cosecant θ = 1 / sine θ = hypotenuse / opposite leg
secant θ = 1 / cosine θ = hypotenuse / adjacent leg
cotangent θ= 1 tangent θ = adjacent leg / opposite leg.
Now, we are told that the angle formed is 53.13°. Since the options are either arctan or arccos, we will use them to verify the angles;
cos 53.13° = 0.6
tan 53.13° = 1.33
They are both positive and it means both x and y values are positive since we are told that it involves the positive x-axis.
Thus, y/x cannot be negative or -3/4 as given.
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The note F# has a frequency of 1,480 hertz. The note B has a frequency of 988 hertz. Find the ratio of F# to B to two decimal places. Express the answer in integer-ratio form.
answer is a fraction.
The ratio of F# to B to two decimal places is 1.50:1.
What is ratio?A ratio is simply used to compare two things or numbers.
In this case, the note F# has a frequency of 1,480 hertz and the note B has a frequency of 988 hertz.
The ratio of F to B will be:
= 1480 / 988
= 1.50
The ratio is 1.50:1.
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Answer:
3/2
Step-by-step explanation:
The following data represent the number of people aged 25 to 64 years covered by health insurance (private or government) in 2018. Approximate the mean and standard deviation for age.
Age: 25-34 35-44 45-54 55-64
Number: 24.3 36.1 36.7 20.9
(Millions)
The mean age is:
The standard deviation is:
The mean age is equal to: 44.09.
The standard deviation is equal to: 10.07.
How to determine the mean age and standard deviation?First of all, we would determine the median of each class interval as follows:
Median 1 = (25 + 34)/2 = 29.5
Median 2 = (35 + 44)/2 = 39.5
Median 1 = (45 + 54)/2 = 49.5
Median 1 = (55 + 64)/2 = 59.5
Next, we would calculate the mean age by using this mathematical expression:
Mean age = ∑fx/∑f
Substituting the given parameters into the formula, we have;
Mean age = [(24.3 × 29.5) + (36.1 × 39.5) + (36.7 × 49.5) + (20.9 × 59.5)]/(24.3 + 36.1 + 36.7 + 20.9)
Mean age = [716.85 + 1,425.95 + 1,816.65 + 1,243.55]/118
Mean age = [5,203]/118
Mean age = 44.09.
Now, we can calculate the standard deviation as follows:
Standard deviation, S = √((∑f(xi - μ)²/∑f)
Standard deviation, S = √((24.3 × (29.5 - 44.09)² + (36.1 × (39.5 - 44.09)² + (36.7 × (49.5 - 44.09)² + (20.9 × (59.5 - 44.09)²)/(24.3 + 36.1 + 36.7 + 20.9))
Standard deviation, S = √((5172.70 + 760.56 + 1,074.14 + 4,963.08)/118)
Standard deviation, S = √(11,970.48/118)
Standard deviation, S = √101.5
Standard deviation, S = 10.07.
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What is the equation of the line that passes through the point (-3,-8) and has a slope of 4?
Answer:
[tex]y-8=4(x+3)[/tex]
Step-by-step explanation:
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].
Given m || n
find the value of x and y.
(6x+19)° (2y+1)⁰
(3x+8)°
m
n
A value for x is therefore represented by the first number in an ordered pair, and a value for y is represented by the second.The x- and y-coordinates are the names given to these values.
Find the value of x and y ?The Method of Elimination
To ensure that the two equations have the same leading coefficient, multiply each equation by a reasonable number in step one.
Step 2: Reverse the first equation and subtract the second one.
Step 3: Find y using this new equation.
Step 4: Change Equation 1 or Equation 2 above to y = 2 and then solve for x.
multiply the equation y = x - 6 by -6.
You will then get the equation: 6y = -6x + 36
The two equations will be:
6y = -6x + 36
y = 6x - 19
And you can see that if you add them, you will be able to eliminate x. answer is -6.
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9.8 x 100 =
0.040 x 1,000 =
61 divide 10 =
8.909 x 100 =
Answer:
9.8 * 100 = 980
0.040 * 1000 = 40
61 / 10 = 6.1
8.909 * 100 = 890.9
Step-by-step explanation:
Some students were playing tag on a playground. The number of girls was less than twice the number of boys. If there were 7 girls, how many boys were playing tag? Write an equation and solve.
The number of boys were playing tag are 5.
What is equation?
Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.
Given: Some students were playing tag on a playground. The number of girls was three less than twice the number of boys. If there were 7 girls.
Suppose the number of boys are x,
So, the number of girls are, 2x - 3.
There are 7 girls.
So, 2x - 3 = 7
2x = 10
x = 10/2
x = 5
Therefore, the number of boys were playing tag are 5.
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Samantha owes $25.50 and borrows another $20.00. She pays back $15.25 of her debt and then earns $45.00. Later, Samantha pays back $22.50 of her debt.
How much debt does she still have to pay back? Show your work.
24.) MULTIPLE FORMS Write the decimal 0.5 in two ways. One with a denominator of 10 and one
with a denominator of 100.
Answer:
A denominator of 10: 5/10
A denominator of 100: 50/100
Question 3 of 10
The blue segment below is a diameter of 0. What is the length of the radius
of the circle?
7.7
0
A. 15.4 units
B. 3.85 units
C. 11.55 units
D. 7.7 units
Answer:
I think B. 3.85 units
Step-by-step explanation:
The price of a sweater was reduced from $30 to $18. By what percentage was the price of the sweater reduced?
i need help
The scores on a psychology exam were normally distributed with a mean of 72 and a standard deviation of 6. A failing
grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing
score? Approximately what percentage of the students failed?
The cutoff for a failing score was?
Cut off for the failing score is 60.
Percentage of the student failed is 12.5%.
What is standard deviation?
The term "standard deviation" (or "SD") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
What is normail distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
Given that,
mean = 72
standard deviation = 6
So,
(a) Cutoff score = mean-(2 x standard deviation) [tex]=72-(2\times 6)[/tex][tex]= 72-12[/tex] [tex]=60[/tex].
(b) In a normal distribution, 95% of students fall on both sides of mean in 2 standard deviations range. i.e., [tex]\frac{95}{2} = 47.5[/tex] of students between mean and (mean-2 x standard deviation). So, the percentage of students below 2 standard deviations from mean = 60-47.5 = 12.5%.
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The velocity function of a car is given by v(t) = -3t^2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop. A. a = -6.46 m/s² B. a = -2.76 m/s² C. a = -0.46 m/s² D. a = 2.76 m/s²
The acceleration when the car comes to a full stop is 20.76 meters per square second.
How to find the acceleration?Here we have the velocity function:
v(t) = -3t^2 + 18t + 9
To find the acceleration we need to differentiate with respect to the variable t, so we will get the acceleration:
a(t) = 2*(-3)*t + 1*18
a(t) = - 6*t + 18
Now, the car will come to a stop when the velocity is equal to zero, so we need to solve:
-3t^2 + 18t + 9 = 0
Dividing all by -3 we get:
(-3t^2 + 18t + 9)/-3 = 0
t^2 - 6t - 3 = 0
The solutions are:
[tex]t = \frac{6 \pm \sqrt{(-6)^2 - 4*1*-3} }{2*1} \\\\t = \frac{6 \pm 6.92}{2}[/tex]
We only care for the positive solution:
t = (6 + 6.92)/2 = 6.46
The acceleration at that time is:
a(6.46) = - 6*6.46 + 18 = -20.76
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Use long division to divide.
(x5 + 2x12x² - 5x - 12) = (x² - 3)
The reminder of the equation using the long division method is 70X - 12.
long division method :
Four main steps to solving this problem:
Divide.Multiply.Subtract.Drop down the last digit.[tex]x^2 - 3$\overline{)x^5 + 24x^3- 5x - 12}$( x^3 + 25x\\\\[/tex]
x₅ + 3 x³
(-) (-)
25x³ - 5x - 12
25x³ - 75x
(-) (+)
70x - 12
here
divisor - (x² - 3)
dividend - (x⁵ + 2x12x² - 5x - 12)
quotient - (x³ +25x)
the given question is incomplete the correct question is
Use long division to divide.
(x⁵ + 2x12x² - 5x - 12) / (x² - 3)
The reminder of the equation using the long division method is 70X - 12.
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A dairy farmer wants to mix a 45% protein supplement and a standard 20% protein ration to make 2000 pounds of a high-grade 35% protein ration. How many pounds of each should he use?
The farmer should use 1200 pounds of type 1 mixture and 800 pounds of type 2 mixture to satisfy the given conditions
From given information,
Type 1: 45 percent of protein in the supplement is x pounds
Type 2: 20 percent of the protein in the supplement is (2000 - x) pounds
Also Mixture A 35% of the protein in the supplement is 2000 pounds
According to the equation after removing the percentage sign we have
45x + 20(2000-x)= 35*2000
45x + 40000 - 20x = 70000
25x = 30000
x = 1200
Now for type 2 mixture we have
2000 - 1200 = 800 pounds
Therefore, the farmer should use 1200 pounds of type 1 mixture and 800 pounds of type 2 mixture to satisfy the given conditions
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Calculate total of (A) current assets, (B) plant assets, and (C) stockholders' equity from these selected titles: Cash $7,500, Common Stock $30,000, Retained Earnings $51,000, Prepaid Rent $12,000, Accounts Payable $1,900, Accounts Receivable $6,000, Merchandise Inventory $19,000, Land $16,000, Building $11,000. (Enter your answers as a whole dollar amount.)
The value of the current assets is $44500.
Plants asset = $27000
Equity = $81000
How to calculate the current assets?The value of the current asset will be:
Cash $7,500
Prepaid Rent $12,000
Accounts Receivable $6,000
Merchandise Inventory $19,000,
Current asset = $44500
Plant assets will be:
Land $16,000
Building $11,000.
Plant asset = $16000 + $11000 = $27000
Stockholders equity will be:
Common stock = $30000
Retained earnings = $51000
Equity = $81000
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A group of elementary school students designed a study to find a possible relationship between the number of students absent from school and the overall rate of flu infections in their town. Which of the following is a correct pairing of possible null and alternative hypotheses for this experiment?
The possible pair of null and alternative hypotheses for this experiment is "The null hypothesis is that the flu infection rate has no impact on the number of students absent from school.
The alternative hypothesis is that as the flu infection rate increases, the number of students absent from school also increases."
Hypotheses
Hypotheses refers the testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
Given,
A group of elementary school students designed a study to find a possible relationship between the number of students absent from school and the overall rate of flu infections in their town.
Here we need to find the correct pairing of possible null and alternative hypotheses for this experiment.
Here the given situation is relationship between the number of students absent from school and the overall rate of flu infections in their town.
So, the null hypotheses of this relation is flu infection rate has no impact on the number of students absent from school
And the alternative hypotheses of the relation is defines that the flu infection rate increases, the number of students absent from school also increases.
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Answer:
Step-by-step explanation:
The null hypothesis is that the flu infection rate has no impact on the number of students absent from school.
The alternative hypothesis is that as the flu infection rate increases, the number of students absent from school also increases.
lamp post tilts
toward the Sun at a 2° angle from
the vertical and casts a 25-foot shadow.
The angle from the tip of the shadow
to the top of the lamp post is 45°.
Find the length of the lamp post.
Answer:
the lamp of post is 24 of the same
216. Разложите на множители, а затем вычислите значение выражения
a) a² + ab при а = 6,6, b = 3,4;
б) x2 - ху при х = 0,5, у = 2,5;
в) —5а² — 5ах при а = 4, x = -3
Answer:
Doesn't make a lot of sense. Can you be more specific.
Step-by-step explanation:
Graph the function rule. Tell whether the graph is continuous or discrete. The height h, in inches, of the juice in a 20-oz bottle depends on the amount of juice j, in ounces, that you drink. This situation is represented by the function rule h=8−0.4j.
Upon graphing of the function rule h = 8 - 0.4j, we see that the graph is continuous.
We are given the function as; h = 8 - 0.4j
Let h represent the height in inches on the y-axis and let j represent the amount of juice in ounces on the x-axis.
We are told that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j is an independent variable and h is dependent variable.
The function represents the height of juice after drinking j ounces of juice. Therefore as the juice is being drank, the height of the juice in bottle will change continuously. Therefore, the graph of our given function will be continuous because we can drink fractions of an ounce juice.
The equation of a line in slope-intercept form is given as;
y = mx + b
where;
m is Slope of line
b is y-intercept
If we rewrite our function slope-intercept form of equation, we will get;
h = -0.4j + 8
Thus;
Slope = -0.3
y-intercept = 8.
The graph is as plotted in the attached file
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An airplane travels 3582 kilometers against the wind in 6 hours and 4482 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
Answer: Let us assume speed of jet in still air =x
speed of wind =y
Jet flying against the wind
Relative speed of the jet = speed of jet in still air -speed of the wind=x-y
distance covered =3426
time =6 hours
distance = speed * time
3426=(x-y)*6
x-y =3426/6
x-y=571——(1)
Jet flying with the wind
Relative speed of the jet = speed of jet in still air +speed of the wind=x+y
distance covered =4026
time =6 hours
distance = speed * time
4026=(x+y)*6
x+y =4026/6
x+y=671———-(2)
solving 1 and 2 we get
x+y=671
x-y=571
x=621
y=50
speed of jet in the still air =x= 621 miles per hour
Step-by-step explanation:
The formula W=0.86g^2-0.01g+5.9 models the weight, W, in ounces, for a cat who is fed g grams per day of a special food. According to the formula, how much will a cat weigh when it is fed 13 grams of the special food per day? Round to the nearest hundredth.
Weight of cat when 13 grams food is fed is 151.11 ounces.
Explain equationEquations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity.
Given, the formula for weight,
W = 0.86[tex]g^{2}[/tex] - 0.01g + 5.9
= 0.86[tex](13^{2} )[/tex] - 0.01*13 + 5.9
= 0.86*169 - 0.13 + 5.9
= 145.34 - 0.13 + 5.9
= 151.11 ounces
Therefore, the weight of the cat will be 151.11 ounces.
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The resistance of a thermistor, a device used to monitor the temperature inside an engine, changes with temperature. The resistance of the thermistor is given by R(t) = t3 + 5, where R is measured in ohms and t is the temperature in °C. What is the average rate of change of resistance per degree of temperature change between 0°C and 2°C?
A.
4 ohms/°C
B.
8.5 ohms/°C
C.
11 ohms/°C
D.
17 ohms/°C
Answer: In photo below
You're Welcome :)
The average rate of change of the resistance of the thermistor for each degree change in the temperature, when the temperatures changes from 0 °C and 2 °C is A. 4 ohms/°C
What is the average of a set of values?The average is calculated by adding the values in the dataset then dividing the result by the count of the numbers or values in the set. The average is also known as the arithmetic mean.
The function for finding the resistance of the thermistor is; R(t) = t³ + 5
The unit of the R = Ohms
The unit of t = Degrees Celsius, °C
The resistance of the thermistor when the temperature is t = 0 °C is found as follows;
R(0) = 0³ + 5 = 5
Therefore;
When the temperature is 0 °C the resistance of the thermistor is 5 Ohms
When the temperature is t = 2 °C, we have;
R(2) = 2³ + 5 = 13
The resistance of the thermistor at t = 2 °C is 13 Ohms
The average rate of change of a function, f(x), is found using the formula;
[tex]A(x) = \dfrac{f(x_2) - f(x_1) }{x_2-x_1}[/tex]
The average rate of change of the resistance per degree change in the temperature, between the temperature interval of 0 °C and 2 °C is therefore;
[tex]A(x) = \dfrac{R(2) - R(0)}{2 - 0}[/tex]
Which gives;
[tex]A(t) = \dfrac{13 -5}{2 - 0}= 4[/tex]
The average rate of change of the resistance of the thermistor between the temperatures of t = 0 °C and t = 2 °C is 4 Ohms/°C
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For d the question is asking after four months, the heat is turned off. The excess amount, electricity from the solar panels begins to build back up according to the function. E(d)=38d+500. How do you interpret the 38 in the 500 and this model, we’re doing our presents the number of days since the heat was turned off. How would I solve this?
From the equation E(d) = 38d + 500, The initial electricity is 500W and the build up is 38W per day
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
The standard equation of a straight line is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let E represent the electricity from the solar panels after d days.
Since:
E(d) = 38d + 500
The y intercept is 500 and the slope is 38
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6) Tomás está haciendo compras en el supermercado. Primero eligió
una bandeja con naranjas cuya etiqueta dice 1.350 g. ¿Cuántos
gramos más debe comprar si quiere llegar a 5 kg?
With the help of unitary method it can be found out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.
It is given to us that -
Tomás first chose a tray with oranges whose label says 1,350 gram
We have to find out more grams of oranges that he should buy if he wants to reach 5 kilogram.
We know that
1 kilogram = 1000 grams
=> 1000 grams = 1 kilogram ----- (1)
By unitary method, we can find out the number of kilograms equivalent to 1350 grams of oranges.
From equation (1), we have
1000 grams = 1 kilogram
=> 1350 grams = (1/1000) * 1350
=> 1350 grams = 1.35 kilograms ----- (2)
Now, from equation (2), we can see that Tomás first chose 1,350 grams of oranges which is equal to 1.35 kilograms of oranges.
This implies that the more kilograms of oranges that Tomás has to buy to reach 5 kilograms is given by -
(5 - 1.35) kilograms
= 3.65 kilograms
From equation (1), we have
1 kilogram = 1000 grams
=> 3.65 kilograms = 3.65 * 1000 grams
=> 3.65 kilograms = 3650 grams.
Thus, by solving through unitary method we find out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.
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