The quotient of a number and 0.2 is -2.6
Quotients are used to represent the division of numbers
The number is -0.52
Let the number be represented with x.
So, the quotient of a number (x) and 0.2 is -2.6 is represented as:
[tex]\frac x{0.2} = -2.6[/tex]
Multiply both sides of the equation by 0.2
[tex]0.2 * \frac x{0.2} = -2.6 * 0.2[/tex]
Evaluate the quotient, on the left hand side
x = -2.6 * 0.2
Evaluate the product on the right hand side
x = -0.52
Hence, the number is -0.52
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Find the slope of the line.
You have a gift card for your favorite clothing store for the amount of $60. You have found a shirt you want to buy that costs $15. If you don't want to spend more than the amount of the gift card, which of the following inequalities could be used to determine the amount you have left to spend?
Answer:
D. x + 15 ≤ 60
Step-by-step explanation:
Let x be the amount you have left to spend after you purchase the shirt.
We must add to x the cost of the shirt, $15. This gives us x+15.
We only have $60 to spend; this means we can spend anything up to and including $60. This means we want "less than or equal to." This gives us the inequality
x+15 ≤ 60
The inequality of the form x + 15 ≤ 60 is the correct choice.
What is an inequality ?An inequality is a comparison between two non equal expression or terms or numbers.
According to the given question You have a gift card for your favorite clothing store for the amount of $60.
You have found a shirt you want to buy that costs $15 but you don't want to spend more than the amount of the gift card.
Assuming the amount you will have is x dollars.
∴ x + 15 ≤ 60
As x ≤ 60 - 15
x ≤ 45.
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The function f(x) = x2 + 5x – 6 is shifted 4 units to the left to create g(x). What is g(x)?
Answer:
g(x)=(x+4)^2+5(x+4)-6
What dose 0.07x1.22 eaqual
Final answer:
When multiplying 0.07 by 1.22, the product is 0.0854. This result is calculated by first multiplying the numbers as whole numbers and then placing the decimal point so that the total number of decimal places in the product matches the sum of the decimal places in the factors.
Explanation:
To calculate the product of 0.07 and 1.22, you follow the standard multiplication procedure for decimals:Multiply as if the numbers were whole numbers; ignore the decimal points for a moment.Count the total number of decimal places in both of the numbers you're multiplying. In 0.07, there are two decimal places. In 1.22, there are two decimal places as well.Add the number of decimal places together. In this case, 2 (from 0.07) plus 2 (from 1.22) equals 4 decimal places in total.Perform the multiplication without considering the decimal, which gives you 7 * 122 = 854.Place the decimal point in the answer (854) so that there are 4 decimal places, giving you 0.0854.Therefore, 0.07 multiplied by 1.22 equals 0.0854.
Final answer:
When multiplying 0.07 by 1.22, we first ignore the decimals and multiply 7 by 122 to get 854, and then we place the decimal point so the result has the same number of decimal places as the sum of the factors, resulting in 0.0854.
Explanation:
To find the product of two decimal numbers, you multiply them just as you would with whole numbers, taking care to place the decimal point in the correct position in the final answer. For the multiplication of 0.07 by 1.22, you perform the multiplication ignoring the decimals first, and then place the decimal in the final answer so that the total number of decimal places equals the sum of the decimal places in the factors.
Multiplying 7 by 122 equals 854. Since 0.07 has two decimal places and 1.22 has two decimal places, the product must have four decimal places. Therefore, the correct placement of the decimal point in 854 would be after four digits from the right, which gives us a final answer of 0.0854.
Does anyone know a rule that work for all of these
1/4 of 12 bottles of water
Evaluate using the order of operations. 54 + (9.2 - 1.413)
Yikes mctugg bought 1/2 pounds of potato salad. He ate 2/3 of it for lunch. How much potato salad was left for an afternoon snack
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50 POINTS
Identify the explicit function for the sequence in the table
The diagram shows an isosceles triangle. All the measurements are in cm. Work out the perimeter of the triangle.
How do I achieve the other 3 marks (putting what shows in the box got me 1/4 marks)? Putting "cm" after the numbers did nothing.
The final mark you can get by substitute the 6 to the x which you get the total of 38 because you have to calculate the perimeter of the isosceles triangle. You both literally helped me to get the full marks on Mathswatch Thank you!
If the equation y = 15x + 2 is changed to y = 15x - 4, how will the graph of the line change?
The graph of the line change is, It will shift down 6 units.
The given function is,
y = 15x + 2
Now, We want to find how the graph of this function will change if the function is transformed to
y = 15x -4
We rewrite this function in terms of the first one to get:
y = 15x + 2 + (-6)
Hence, the function with shift down 6 units.
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What is the value of a in the equation 4a + 3(a + 1) = 24?
write the following equation in standard form. x^5+2x^3+6x+1/5
The standard form is x⁵ + 2x³ + 6x + [tex]\frac{1}{5}[/tex].
To write the given equation x⁵ + 2x³ + 6x + [tex]\frac{1}{5} \\[/tex] in standard form, follow these steps:
Identify and list all terms in the polynomial: x⁵, 2x³, 6x, and [tex]\frac{1}{5}[/tex].Arrange the terms in descending order based on the exponent of x:x⁵ + 2x³ + 6x + [tex]\frac{1}{5}[/tex]Ensure all coefficients and constants are in standard form:The polynomial in standard form is: x⁵ + 2x³ + 6x + [tex]\frac{1}{5}[/tex].How many solutions does this linear system have?
An orchard has 864 orange trees. The number of rows exceeds the number of trees per row by 5 . How many trees are there in each row?
Final answer:
Using a quadratic equation, we found that there are 24 orange trees in each row of the orchard.
Explanation:
To determine how many orange trees are there in each row, we will set up an equation based on the information provided. Let's let x represent the number of trees per row. According to the problem, the number of rows is x + 5. Since the total number of trees in the orchard is 864, we can create the following equation:
x * (x + 5) = 864
To solve this quadratic equation, we need to find the value of x that satisfies the equation:
First, expand the left side of the equation: [tex]x^{2}[/tex] + 5x.
Write the equation in standard form: [tex]x^{2}[/tex] + 5x - 864 = 0.
Factor the quadratic equation: (x + 36)(x - 24) = 0.
Solve for x: x = -36 or x = 24.
Since we cannot have a negative number of trees per row, we disregard x = -36.
Therefore, there are 24 trees in each row.
Jackson is flying at a constant rate of 500 mph from New York, New York, to Austin, Texas, which is a distance of 1,750 miles. If the distance Jackson has traveled in miles is a function of time in hours he has been flying, determine an appropriate domain and range for this problem situation.
The domain of the function is [tex][0,3.5][/tex] and the range of the function is [tex][0,1750][/tex].
Speed [tex]= 500[/tex] mph
Distance [tex]= 1750[/tex] miles
Distance [tex]=[/tex] Speed [tex]\times[/tex] Time
The distance Jackson has traveled in miles is a function of time in hours he has been flying.
[tex]f(t)=500t.[/tex]
For maximum distance, [tex]f(t)=1750[/tex] miles.
[tex]1750=500t.[/tex]
[tex]t=\frac{1750}{500}[/tex]
[tex]t=3.5[/tex] hours
So, domain [tex]= [0,3.5][/tex]
Range [tex]= [0,1750][/tex]
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At your birthday party, 5/8 of the 24 guests were relatives. How many relatives were at your party?
hello i need help in this, someone pls!!!
Find counter example to disprove the conjecture:
if the quotient of two numbers is positive, then the two numbers must be positive
Using the rule of 72, mc003-1.jpg, how long will it take for the principal to double with an annual compound interest rate of 6%?
6 years
9 years
12 years
15 years
Answer:
Option C. 12 years
Step-by-step explanation:
Let principal amount taken = x
We know the formula of compound interest
Final amount = Principal amount×[tex](1+\frac{r}{n})^{nt}[/tex]
Where r = rate of interest (per year)
n = number of times compounded (annually)
t = time in years (years)
Here we have to find the time in which principal amount is doubled.
From the question r = 6% = .06
n = 1
Principal amount = P
Final amount = 2P
Now we put these values in the formula
[tex]2P=P(1+.06)^{t}[/tex]
[tex]2=(1.06)^{t}[/tex]
Now we take log on both the sides
[tex]log(2)=log(1.06)^{t}[/tex]
0.301 = tlog(1.06)
0.301 = t×(.025)
[tex]\frac{0.301}{0.25}=t[/tex]
t = 12 years.
Option C. 12 years is the answer.
Find the Slope A(4,6) B(-8,-3)
Which number line shows the solution to −6 − (−4)? A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 10 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to 6 is shown. Above this, another arrow pointing from 6 to 10 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to 6 is shown. Above this, another arrow pointing from 6 to 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
-6 -(-4) = -6 +4 = -2
So answer is:
A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
Answer:
The correct option is B) A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
Step-by-step explanation:
Consider the provided expression.
−6 − (−4)
Open the parentheses and change the sign.
−6 − (−4)
−6 + 4
Subtract the numbers.
−2
Now draw this on number line.
First draw a number line is shown from −10 to 0 to 10. with scale of 2 unit on either side of the number line. Draw an arrow pointing from 0 to −6 Which show −6. Above this, another arrow pointing from −6 to −2 which shows −6 − (−4) = −2. A vertical bar is shown at the tip of the arrowhead of the top arrow.
The required number line is shown in the figure 1.
Hence, the correct option is B) A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
Professor's annuity corp. offers a lifetime annuity to retiring professors. for a payment of $90,000 at age 65, the firm will pay the retiring professor $850 a month until death.
a. if the professor's remaining life expectancy is 15 years, what is the monthly interest rate on this annuity?
The monthly interest rate on this annuity is approximately 0.4318%.
Explanation:To find the monthly interest rate on the annuity, we need to use the present value formula for an annuity:
PV = A * (1 -[tex](1+r)^{(-n)[/tex]) / r
Where PV is the present value, A is the monthly payment, r is the monthly interest rate, and n is the total number of payments. In this case, PV = $90,000, A = $850, and n = 15 (since the professor's remaining life expectancy is 15 years).
By plugging in these values and solving for r, we can find the monthly interest rate on the annuity.
$90,000 = $850 * (1 - [tex](1+r)^{-15)[/tex] / r
After solving this equation, we find that the monthly interest rate on this annuity is approximately 0.4318%.
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The monthly interest rate is approximately 0.58%.
To determine the monthly interest rate on the annuity, we need to solve for the rate that equates the present value of the annuity payments to the initial payment of $90,000. The payments of $850 are made for the expected life of 15 years, which translates to 180 monthly payments.
The present value (PV) of an annuity can be calculated using the formula:
[tex]PV = Pmt * [(1 - (1 + r)^{-n}) / r][/tex]
Where:
Pmt = $850 (monthly payment)
r = monthly interest rate
n = 180 (total number of payments)
Given PV = $90,000, we need to solve for r:
$90,000 = $850 × [(1 - (1 + r)^-180) / r]
This requires solving the equation iteratively or using a financial calculator, as it's a non-linear equation. By trial and error or using a financial calculator or spreadsheet:
We find that r ≈ 0.0058 or 0.58%
Thus, the monthly interest rate on this annuity is approximately 0.58%.
A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
Answer:
Sorry that I’m late, answer is C. y=7x
Step-by-step explanation:
14/2 = 7
28/ = 7
Simplify and determine the coefficient of (-2/3x)(3y)(-2x). -4 1 4
Which graph represents the solution set of the system of inequalities?
(1st picture is question and 1st set of answers 2nd picture is 2nd set of answers.
Determine the solution set of (2x - 5)2 = 11.
Taking square root on both sides, that becomes 2x - 5 = (+/-) √11
Then:
2x = (+/-)√11 + 5
x = [5 +/- √11 ] / 2
x = 5/2 +/- (√11)/2
That is, x = 5/2 +(√11)/2 and x = 5/2 - (√11)/2
After driving for 2.2 hours (2 hours and 12 mintues), marcos' total distance traveled was 153 miles. at what constant speed (in miles per hour) would he have to travel for the last 5 minutes in order to complete the 155 mile drive in 2 hours and 17 minutes?
Answer:
24 miles per hour.
Step-by-step explanation:
So in order to calculate this you just need to use the formula for the speed:
Speed=Distance/time
Speed= 2 miles/ 5 minutes
Speed= 2 miles/,083 hours
Speed= 24
So the speed at the final 5 minutes will be 24 miles per hour.
The circumference of a circular field is
260.62 yards. What is the diameter of the field? Use 3.14 for π and do not round your answer.
The diameter of the field is 83 yards.
Explanation:To find the diameter of a circular field, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Given that the circumference of the field is 260.62 yards, we can solve for the radius by dividing the circumference by 2π.
Using the value of π as 3.14, we can calculate:
260.62 / (2 * 3.14) = 41.50 yards
Since the diameter of a circle is twice the radius, the diameter of the field is 2 * 41.50 = 83 yards.