Answer:
x=-6
Step-by-step explanation:
Answer: x= -6
Step-by-step explanation:
You combine the 2 expressions
8x+8=5x-10
move the smallest variable
3x+8=-10
and do what you would normally do
3x=-18
/3
x=-6
Which linear equation shows a proportional relationship? y equals one seventh times x minus 2 y equals negative one seventh times x y = −7x 3 y = 7
The linear equation that is also a proportional relationship is the second option:
y = (-1/7)x
Which linear equation shows a proportional relationship?A linear relation is of the general form:
y = ax + b
Where a is the slope and b is the y-intercept.
And a proportional relation is a linear relation such that the y-intercept is zero, so we will have:
y = ax
Here the linear relations in the options are:
y = (1/7)x - 2
y = -(1/7)x
y = -7x + 3
y = -7
The only option that shows a proportional relatiopn is the second one, where we have a slope and no y-intercept.
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Complete the table of values for equation y=5-2x
The required table of values for equation y=5-2x is;
x | y
0 5
1 3
2 1
3 -1
Functions and valuesTables of values are values used to represent functions.
Given the linear function expressed as y = 5 - 2x, we are to form a tables of values for the function.
Using the values of x = 0, 1, 2, and 3
If x = 0
y = 5 - 2(0)
y = 5
If x = 1
y = 5 - 2(1)
y = 3
If x = 2
y = 5 - 2(2)
y = 1
If x = 3
y = 5 - 2(3)
y = -1
Hence the required table of values for equation y=5-2x is;
x | y
0 5
1 3
2 1
3 -1
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The area of a square poster 26 inch. 2. Find the length of one side of the poster to the nearest tenth of an inch.
Answer:
6.5 inches
Step-by-step explanation:
Divide 26 by 4
26/4=6.5
The length of one side of the poster to the nearest tenth of an inch is 5.1 inches.
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
Given; The area of a square poster 26 inch
We need to find the length of one side of the poster to the nearest tenth of an inch.
The area of a square would be S^2
26 = S^2
s = sqrt(26) = 5.099
Then rounded to nearest tenth = 5.1 inches
Hence, the length of one side of the poster to the nearest tenth of an inch is 5.1 inches.
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Natasha starts with $45 in her savings account, and each month she adds $6. Sal starts with $55 in his savings account, and each month he adds $4.
How many months will it take for Natasha to have more money in her savings account than Sal in his?
It will take 6 months for Natasha to have more money in her savings account than Sal in his.
Linear functionsTo determine how many months it will take for Natasha to have more money in her savings account than Sal in his, the following calculation must be performed, through a linear function:
45 + (6X) = Natasha55 + (4X) = Sal55 - 45 = 106 - 4 = 210 / 2 = 545 + 6 x 5 = 45 + 30 = 7555 + 4 x 5 = 55 + 20 = 75Therefore, it will take 6 months for Natasha to have more money in her savings account than Sal in his.
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Simplify the following expression by combining like terms. Select the most simplified expression
4(5m + 3) + 2m
A: 20m + 6 + 2m
B: 22m +6
C: 20m + 12 + 2m
D: the 22m + 12
Answer:
It is D
Step-by-step explanation:
Distribute:
=(4)(5m)+(4)(3)+2m
=20m+12+2m
Combine Like Terms:
=20m+12+2m
=(20m+2m)+(12)
=22m+12
PLEASE I NEED HELP RIGHT AWAY
What is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1) ?
Responses
y+4=11/6(x+1)
=
y+1=6/11(x+4)
y−1=6/11(x−4)
y+1=6/7(x+4)
y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).
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
The given two points are (7, 5) and (−4, −1)
m=-1-5/-4-7
=-6/-11
=6/11
The point slope intercept form is y- y₁=m(x-x₁) through (-4,-1)
y-(-1)=6/11(x-(-4))
y+1=6/11(x+4)
Hence, y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).
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many elementary school students in a school district currently have ear infections. a random sample of children in two different schools found that 11 of 40 at one school and 12 of 30 at the other have ear infections. at the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools?
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools.
To determine if there is sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools, we can use a two-sample z-test for the difference in proportions.
The null hypothesis is that there is no difference between the proportions of students with ear infections at the two schools, while the alternative hypothesis is that there is a difference.
Let p1 be the proportion of students with ear infections at the first school and p2 be the proportion at the second school. The test statistic is given by:
z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))
where p_hat is the pooled proportion, n1 and n2 are the sample sizes from the first and second schools, respectively.
The pooled proportion is given by:
p_hat = (x1 + x2) / (n1 + n2)
where x1 and x2 are the number of students with ear infections in each school.
Using the given data, we have:
n1 = 40, n2 = 30
x1 = 11, x2 = 12
p1 = x1/n1 = 11/40 = 0.275
p2 = x2/n2 = 12/30 = 0.4
p_hat = (x1 + x2) / (n1 + n2) = (11 + 12) / (40 + 30) = 0.355
The test statistic is:
z = (0.275 - 0.4) / sqrt(0.355 * 0.645 * (1/40 + 1/30)) = -1.197
Using a standard normal table or calculator, the p-value for a two-tailed test with a test statistic of -1.197 is approximately 0.231.
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Indeterminate form [0^0]: Calculate the following limits using L'Hospital's Rule.
lim tanx^sinx
x-> 0+
With the way the problem is written on my homework, I'm not sure if it's (tanx)^sinx or tan(x^sinx). Answers to both methods would be helpful.
When interpreting the expression as \((tanx)^{(sinx)\), the limit using L'Hospital's Rule is -∞ as x approaches 0+. However, when interpreting the expression as\(tan(x^{sinx})\), the limit is not well-defined due to the indeterminate form of 0^0.
To calculate the limit using L'Hospital's Rule, let's consider both interpretations of the expression and find the limits for each case:
Case 1: lim\((tanx)^{(sinx)\) as x approaches 0+
Taking the natural logarithm of the expression, we have:
\(ln[(tanx)^{(sinx)}] = sinx * ln(tanx)\)
Now, we can rewrite the expression as:
\(lim [sinx * ln(tanx)]\)as x approaches 0+
Applying L'Hospital's Rule, we differentiate the numerator and denominator:
\(lim [(cosx * ln(tanx)) + (sinx * sec^{2}(x))] / (1 / tanx)\) as x approaches 0+
Simplifying the expression:
\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * tanx\) as x approaches 0+
\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * (sinx / cosx)\) as x approaches 0+
\(lim [(cosx * ln(tanx) + sinx * sec^{2}(x)) / cosx] * sinx\) as x approaches 0+
\(lim [ln(tanx) + (sinx / cosx) * sec^{2}(x)] * sinx\) as x approaches 0+
\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+
Since lim ln(tanx) as x approaches 0+ = -∞ and\(lim (tanx * sec^{2}(x))\) as x approaches 0+ = 0, we have:
\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+ = -∞
Therefore, the limit of \((tanx)^{(sinx)\) as x approaches 0+ using L'Hospital's Rule is -∞.
Case 2: lim\(tan(x^{sinx})\)as x approaches 0+
We can rewrite the expression as:
lim\(tan(x^{(sinx)})\) as x approaches 0+
This expression does not have an indeterminate form of \(0^0\), so we do not need to use L'Hospital's Rule. Instead, we can substitute x = 0 directly into the expression:
lim \(tan(0^{(sin0)})\) as x approaches 0+
lim\(tan(0^0)\)as x approaches 0+
The value of \(0^0\) is considered an indeterminate form, so we cannot determine its value directly. The limit in this case is not well-defined.
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Tell whether the equation has one, zero, or infinitely many
solutions.
4x + 2 = 4x - 5
a. if the value of land in an area is increasing 9 percent a year, how long will it take for property values to double? (round your answer to 1 decimal place.)
it will take approximately 7.7 years for property values to double with a 9 percent annual increase.
To determine how long it will take for property values to double with an annual increase of 9 percent, we can use the concept of the compound interest formula. In this case, the property values are growing exponentially over time.
The formula to calculate the doubling time is:
t = (log(2) / log(1 + r))
Where:
t = time (in years)
r = annual growth rate as a decimal (9 percent = 0.09)
Plugging in the values into the formula, we can find the time it takes for property values to double:
t = (log(2) / log(1 + 0.09))
Calculating this, we find:
t ≈ 7.69 years
Therefore, it will take approximately 7.7 years for property values to double with a 9 percent annual increase.
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Use the following information to sketch a graph of the original function, f(X) write the equations of any asymptotes. - lim x→[infinity]
f(x)=5 - f ′
(x)>0 on (−2,1)∪(1,[infinity]) - f ′
(x)<0 on (−[infinity],−2) - f ′′
(x)>0 on (−[infinity],−4)∪(1,4) - f ′′
(x)<0 on (−4,−2)∪(−2,1)∪(4,[infinity])
The equations of the vertical asymptotes can be given as x = -4, -2, and 1. The function f(x) does not have any horizontal asymptotes.
The function, f(x) is given as f(x)=5 - f ′(x)>0 on (−2,1)∪(1,[infinity]) f ′(x)<0 on (−[infinity],−2)f ′′(x)>0 on (−[infinity],−4)∪(1,4)f ′′(x)<0 on (−4,−2)∪(−2,1)∪(4,[infinity])
To sketch the graph of the original function, we have to determine the critical points, intervals of increase and decrease, the local maximum and minimum, and asymptotes of the given function.
Using the given information, we can form the following table of f ′(x) and f ′′(x) for the intervals of the domain.
The derivative is zero at x = -2, 1.
To get the intervals of increase and decrease of the function f(x), we need to test the sign of f ′(x) at the intervals
(−[infinity],−2), (-2,1), and (1,[infinity]).
Here are the results:
f′(x) > 0 on (−2,1)∪(1,[infinity])f ′(x) < 0 on (−[infinity],−2)
As f ′(x) is positive on the intervals (−2,1)∪(1,[infinity]) which means that the function is increasing in these intervals.
While f ′(x) is negative on the interval (−[infinity],−2), which means that the function is decreasing in this interval.
To find the local maximum and minimum, we need to determine the sign of f ′′(x).
f ′′(x)>0 on (−[infinity],−4)∪(1,4)
f ′′(x)<0 on (−4,−2)∪(−2,1)∪(4,[infinity])
We find the inflection points of the function f(x) by equating the second derivative to zero.
f ′′(x) = 0 for x = -4, -2, and 1.
The critical points of the function f(x) are -2 and 1.
The inflection points of the function f(x) are -4, -2, and 1.
Hence, the equations of the vertical asymptotes can be given as x = -4, -2, and 1.The function f(x) does not have any horizontal asymptotes.
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If anyone knows the answer to this please answer.
4(8x+6)−7x
Stephan considers the pizza in
problem 1. He wonders if an 18-inch
diameter pizza, whose toppings cover a 14-inch diameter circle, will have more, less, or the same percentage of area not covered in toppings.
Help him find the answer.
The percentage of the area not covered in toppings is 30.6%.
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
The radius of the whole pizza is 9 in. the radius of the portion of the pizza covered by toppings is 7 in.
The area of a circle is πr^2, where r is the radius. the fraction of the pizza covered by toppings is ;
f - covered = [π(7 in)^2] / [π(9 in)^2]
= 100/144 = 50/72
= 25/36
where the π's and the inches canceled, leaving a pure fraction.
= 1 - 25/36
= 36/36 - 25/36
= 11/36 ≈ 0.306 % not covered
= f_not covered x 100%
= 30.6%
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For box plot data where Q1 = 200, Q2 = 250, and Q3 = 290, the
IQR
The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.
Given that,
For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290
We have to find the data of IQR.
We know that,
IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.
IQR Formula is Q₃ - Q₁
So,
Q₃ = 290
Q₁ = 200
Then ,
IQR = Q₃ - Q₁
IQR = 290 - 200
IQR = 90
Therefore, The value of IQR is 90.
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Los boxeadores profesionales, cuyo peso varía entre 122 lb y 126 lb, pertenecen a la categoría peso Pluma. ¿Cuál es el menor peso en kilogramos que debe tener un boxeador para pertenecer a la categoría peso Pluma? ¿Cuál es el mayor? ¿Se puede considerar a un boxeador que pese 57 kg como peso Pluma?
A boxer must weigh at least 55.34 kg and no more than 57.15 kg to be considered a featherweight. Consequently, a boxer who weighs 57 kg is not a featherweight.
Featherweight is one of the lighter weight categories in professional boxing. The typical weight range for these boxers is 126 lbs (55.34 kg) to 122 lbs (57.15 kg). This weight limit allows smaller fighters to compete against larger ones, levelling the playing field.
Boxers who weigh more than 57.15 kg are ineligible to compete in the Featherweight division, regardless of how few kilograms separate them. Boxers must be aware of these restrictions because they are strictly enforced by boxing organizations and referees. The Featherweight division in professional boxing is significant because it gives smaller boxers a chance to compete in the sport.
Boxers must adhere to the weight restrictions set by the boxing commission in order to compete in Featherweight matches. This allows for fair and equal competition, and ensures that all boxers are competing on an even playing field.
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Solve 67 x 92 Using Partial Product
Answer:
6164
Step-by-step explanation:
A carpenter needs 8.5 feet of rope for a project. how much will the carpenter spend if the rope costs $4.57 per foot? $34.12 $38.85 $59.41 $388.45
Answer:
$38.85
Step-by-step explanation:
cost = unit rate × amount
cost = $4.57/ft × 8.5 ft
cost = $38.85
The carpenter spend is $38.85.
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary MethodFirst, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
given:
length of rope= 8.5 feet
cost per foot= $4.57
So,
Total cost of rope
= $4.57/ft × 8.5 ft
= $38.85
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What are the values of x and y?
Answer:
x = 8 +8√3 ≈ 21.856y = 12 +4√3 ≈ 18.928Step-by-step explanation:
Given a diagram of two "special" triangles, you want to know the measures of x and y.
Special trianglesThe right triangles with angles 30°-60°-90° and 45°-45°-90° are considered "special" because they have side lengths in ratios that can be expressed in a simple form.
The side lengths of a 30°-60°-90° triangle have ratios 1 : √3 : 2.
The side lengths of a 45°-45°-90° triangle have ratios 1 : 1 : √2.
ApplicationThe ratio of x to y is the ratio of the two longer sides of the 30°-60°-90° triangle:
y : x = √3 : 2
The unmarked segment at the bottom edge of the figure will have length x/2. The ratio of side lengths of the 45°-45°-90° triangle is then ...
1 : 1 = (8 +x/2) : y
These relations give us two equations in x and y:
2y = (√3)xy = (8 +x/2)SolutionSubstituting the latter expression for y into the first equation gives ...
2(8 +x/2) = (√3)x . . . . . . substitute for y
16 +x = √3x . . . . . . . . . . eliminate parentheses
16 = x(√3 -1) . . . . . . . . . subtract x and factor
x = 16/(√3 -1) . . . . . . . . divide by the coefficient of x
x = 16(√3 +1)/2 = 8(√3 +1)
x = 8 +8√3 ≈ 21.856
Then the value of y is ...
y = 8 +(8 +8√3)/2 = 8 +4 +4√3
y = 12 +4√3 ≈ 18.928
please help with this question
Answer:The answer to this question would be "1470"To find the volume, all you need to do is Multiply the length, width, and height of the object together and you can find the Volume.Hope this helps, Please mark as Brainliest.
Step-by-step explanation:have a good day.
Answer:
7 1/2 * 15 *14=1575
1575 is the answer
Draw the graph of the equation
g(x) = -3x +2.
You can refer to the section "Drawing Graphs in Mobius" in the unit "Introduction to
Mobius" for
practice in drawing graphs of lines in Mobius.
Part a: Find one point on the line. Often it's smart to start with the value x = 0 because multiplying by
and adding 0 are easy. In other words, find the y-intercept.
The point (0, Number ) is on the line g(x) = -3x + 2.
Part b: Find a second point on the line. Often it's easier to continue with the value x = 1 as multiplying
by and adding 1 are pretty easy.
The point (1, Number ) is on the line g(x) = -3x +2.
Use DESMOS to graph any function online.
The picture shows the graph of g(x) = -3x + 2.
Mrs. Smith has 6 activity tables she wants to line up side by side in her classroom. In how many ways can she arrange all 6 tables? Show your work. If she only wants to have 4 of the tables set up, in how many ways can she choose the tables she wishes to have set up? Show your work.
The number of ways to arrange all six tables is given as follows:
720 ways.
The number of ways to have four of the tables is given as follows:
360 ways.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
\(N = n_1 \times n_2 \times \cdots \times n_n\)
To arrange the six tables, the number of ways is given as follows:
N = 6 x 5 x 4 x 3 x 2 x 1 = 720 ways.
To choose four tables, the number of ways is given as follows:
N = 6 x 5 x 4 x 3 = 360 ways.
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Convert: 3120 millimeters= centimeters
Explanation:
The question is
Convert
\(3120mm\text{ }to\text{ }cm\)Concept:
To do this, we will use the conversion below
\(1mm=0.1cm\)Hence,
Uidn the conversion rate, we will have trha
\(\begin{gathered} 1mm=0.1cm \\ 3120mm=x \\ cross\text{ multipl, we will have} \\ x=3120\times0.1 \\ x=312cm \end{gathered}\)Hence,
The final amswer is
\(312\text{ }centimeters\)FILL IN THE BLANK. The part of the z-score denoting hundredths is found _____ of the table
The part of the z-score denoting hundredths is found in the interior of the table.
In a standard normal distribution table, also known as a z-table, the z-scores are presented with two parts: the tenths and the hundredths. The tenths are found in the row headings (or sometimes column headings) on the edges of the table, while the hundredths are located in the columns within the interior of the table.
To find a specific z-score in a z-table, first identify the tenths value in the row headings, and then locate the corresponding hundredths value in the columns of the same row. The intersection of the row and column will provide you with the desired probability associated with that particular z-score. The z-table helps in calculating the area under the curve in a standard normal distribution, which is essential for various statistical analyses and probability calculations.
Remember, the z-score is a measure of how far a data point is from the mean in terms of standard deviations. A positive z-score indicates that the data point is above the mean, while a negative z-score indicates that it is below the mean.
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NEED HELP ASAP - Algebra 2
- Explain what a one-to-one function is and how it differs from functions that are not one-to-one.
- Identify two real world examples of a one-to-one function. Explain your reasoning.
Need help please as soon as possible
Answer:
Step-by-step explanation:
13x-6y=10 (1,4)
x=1 y=4
⇒ 13*1-6*4=10
⇒ 13-24=10
⇒ -11≠10
⇒ (1,4) isn`t solution of the equation y=13x-6y
y=-3|x-5|+1 (1,-11)
x=1 y=-11
-11=-3|1-5|+1
-11=-3|-4|+1
-11=-3(4)+1
-11=-12+1
-11≡-11
⇒ (1,-11) is solution of the equation y=-3|x-5|+1
If angle c and angle d are complementary angle and measurement angle c is 13 degrees, find measurement angle d
The measurement of d will be 77 degrees.
Complementary angles are two angles that add up to 90 degrees. In other words, if two angles are complementary, then subtracting one angle's measurement from 90 degrees yields the measurement of the other.
For instance, if angle c is 13 degrees, angle d is 90 - 13 = 77 degrees. This means that the angle d measures 77 degrees.
When two angles are complementary, their measurements add up to 90 degrees, which is why knowing one angle's measurement allows us to find the other angle's measurement.
Complementary angles are two angles that add up to 90 degrees. They are, in other words, two angles that "complement" each other to form a right angle (90 degrees). Complementary angles are used in geometry and trigonometry to solve problems involving triangles and other geometric shapes.
Knowing one complementary angle's measurement allows you to find the other complementary angle's measurement by subtracting it from 90 degrees.
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Which statement describes when the plans are based on the same number of aerobic exercise sessions?
Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.
From the statements that are provided in the question, the statement that best describes when the plans is Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
What is word problem?A word problem are sentences describing a real-life scenario where a problem needs to be solved by mathematical calculation.
Ideally, for the best health benefits, such as increasing strength and aerobic and reduction in heart diseases, it is suggested to do a combination of strength training and aerobic training for at least five times a week.
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week. is the correct statement
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NEED THIS ASAP PLEASE HELP
Bob's Gift Shop sold 200 cards for Mother's Day. One salesman, Bao, sold 2% of the cards sold for Mother's Day. How many cards did Bao sell?
how many Years are in 1,000
The number of years in 1000 days is = 2 . 74 years .
How many Years are in 1,000 day?Division is the arithmetic operation that is used to determine the quotient of a number. Division parts a number into equal parts with another number.
Number of years in 100 days = 1000 / 365
= 2 . 74 years
Here is the complete question:
how many Years are in 1,000 days
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-10 + 7/4p = -38 (I don't understand this question)
Answer:
-16
Step-by-step explanation:
-10 + 7/4p = -38 [multiply the entire equation by 4 to get rid of fraction]
-40 + 7p = -152 [add 40 to each side of equation]
7p = -112
p = -112/7 = -16