using the points 0, 5 and -2, 2 make an equation in slope intercept form
Which of the following pairs of equations has exactly the same solution?(1 point)
−3.2x=0.64 and x/4 =−0.05
⅜ x=1 and ⅓ x=⅛
x/3.2 =1.8 and 1.8x=3.2
− 3/4 x=5/2 and 5/2 x=− 3/4
Answer: The first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05, have exactly the same solution. In both of these equations, the value of x comes out as -0.2.
Step-by-step explanation: Simplifying the first set of equations, we get:[tex]-3.2x=0.64[/tex]
[tex]x=0.64/-3.2[/tex]
x=-0.2
[tex]x/4=-0.05[/tex]
[tex]x=-0.05*4[/tex]
x=-0.2
Simplifying the second set of equations, we get:
[tex]3/8x=1[/tex]
[tex]x=8/3[/tex]
x=2.66
[tex]1/3x=1/8[/tex]
[tex]x=1/8*3[/tex]
x=0.375
Simplifying the third set of equations, we get:
[tex]x/3.2=1.8[/tex]
[tex]x=1.8*3.2[/tex]
x=5.76
[tex]1.8x=3.2[/tex]
[tex]x=3.2/1.8[/tex]
x=1.77
Simplifying the fourth set of equations, we get:
[tex]-3/4x=5/2[/tex]
[tex]x=5/2*-4/3[/tex]
x=-3.33
[tex]5/2x=-3/4[/tex]
[tex]x=-3/4*2/5[/tex]
x=-0.3
Therefore, the first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05 have exactly the same solution.
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the edison electric institute has published figures on the number of kilowatt hours used annually by various home appliances. it is claimed that a vacuum cleaner uses an average of $46$ kilowatt hours per year. if a random sample of $12$ homes included in a planned study indicates that vacuum cleaners use an average of $42$ kilowatt hours per year with a standard deviation of $11.9$ kilowatt hours, do these data suggest that at the $0.05$ significance level the mean annual usage of vacuum cleaners is less than $46$ kilowatt hours? assume the population distribution of usage in kilowatt hours to be normal.
The test statistic is less than - 1.796
Hypothesisi test
H0: μ = 46
Ha: μ < 46
This is a lower tailed test
mean = 42
standard deviation = 11.9
sample size n = 12
The level of significance α = 0.05
degree of freedom df = n - 1 = 12 - 1 = 11
Test statistic = (x - mean)/(standard deviation / √n) = (42 - 46)/(11.9 / √12) = - 1.164
Test statistic = - 1.164
Using t- table, we can observe that the p - value is between 0.10 and 0.15
Using excel we find p - value = P(t < - 1.796)
p value = 0.1344
H0: μ < 46, rejection rule is
Reject H0 if test statistic < - 1. 796
Therefore, we reject the hypothesis as the test statistic is less than - 1.796
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Find the domain and range of the function by the graph. Is the graph discrete or continuous
Domain is the set of values under which a function is defined.
Range is the outcome of all the values of the domain when put in a function.
graphically, the domain is the set of values under which we get some value in the y-axis for a particular function graph .
while the range is the y-coordinate of all the points lying on the graph .
As the graph is not posted by you.
see this graph of the modulus function for instance:
function IxI is defined for every real possible value of xso, R is the domain.
but the range is only positive values of R in y.
and,
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y=-2/7x-7 in standard form
Answer:
Write in standard form.
2x+7y=−49
Step-by-step explanation:
ABCD is a parallelogram. Find mzB.
Answer:
m∠B = 121°
Step-by-step explanation:
[tex]10x-19=9x-5[/tex]
[tex]10x=9x+14[/tex] (add 19 on both sides)
[tex]x=14[/tex] (subtract 9x on both sides)
[tex]9(14)-5 = 126-5=121[/tex]
Answer: m∠B=121°
Step-by-step explanation:
The opposite angles of the parallelogram are equal
Hence,
(10x-19)°=(9x-5)°
10x-19=9x-5
10x-19-9x=9x-5-9x
x-19=-5
x-19+19=-5+19
x=14
Hence,
m∠B=(9(14)-5)°
m∠B=(126-5)°
m∠B=121°
Write an equation of the line passing through point p(3 8) that is parallel to the line y=1/5(x+4).
The equation of the line is y = 1/5(x + 37). The standard equation of a instantly line is y = mx + c, in which m is the gradient, and y = c is the cost in which the road cuts the y-axis.
This range c is known as the intercept at the y-axis. The equation of a instantly line with gradient m and intercept c at the y-axis is y = mx + c. The equation of a instantly line is y=mx+c y = m x + c m is the gradient and c is the peak at which the road crosses the y -axis, additionally referred to as the y -intercept.
Since equation have new line which is parallel y = 1/5(x + 4), and 1/5 is most the gradient for the line y = 1/5(x + 4), this is the new line is 1/5.
Using the equation we can form a line in slope-point form,
[tex]\frac{y-y_{1} }{x-x_{1} } = m[/tex]
where (x₁, y₁) = (3, 8) and m = 1/5
Substituting the values for all variables into the equation, we have
[tex]\frac{y-y_{1} }{x-x_{1} } = m\\\frac{y-8 }{x-3 } = m\\[/tex]
Cross-multiplying. we have
5(y - 8) = x - 3
Expanding the bracket, we have
5y - 40 = x - 3
5y = x - 3 + 40
5y = x + 37
y = 1/5(x + 37)
So, the equation of the line is y = 1/5(x + 37)
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Write a quadratic inequality to represent the area of a stained-glass mosaic that sits under a parabolic arch 10 feet tall and 8 feet wide at the base, if the left side of the base is the origin.
Answer:
To represent the area of a stained-glass mosaic that sits under a parabolic arch, we can use the equation for a parabolic arch, which is of the form
y = a(x - h)^2 + k
where (h,k) is the vertex of the parabola. The width of the parabolic arch at the base is 8 feet, so the vertex of the parabola is located at (4,0). Therefore, the equation for the parabolic arch is
y = a(x - 4)^2
The height of the parabolic arch is 10 feet, so we can represent the area of the stained-glass mosaic as the region where y is between 0 and 10. This can be expressed as the inequality
0 ≤ a(x - 4)^2 ≤ 10
Solving this inequality for x gives us the solution
-2 ≤ x - 4 ≤ 2
which simplifies to
2 ≤ x ≤ 6
Therefore, the quadratic inequality that represents the area of the stained-glass mosaic is
2 ≤ x ≤ 6
Step-by-step explanation:
Answer:
y ≤- 5/8(x - 4)² + 10 andy ≥ 0-------------------------------------------------------
According to given details we have:
The vertex at (8/2, 10) = (4, 10),The parabola opens down,It passes through the origin.The equation for the parabola is y = a(x - h)² + k, where (h, k) is vertex.
Substitute h = 4, k = 10:
y = a(x - 4)² + 10We know y = 0 at x = 0, substitute to find the value of a:
0 = a(0 - 4)² + 100 = a(16) + 1016a = - 10a = - 10/16 = - 5/8So the parabola is:
y = - 5/8(x - 4)² + 10We are looking for the area between the parabola and the x-axis, therefore we need two inequalities:
y ≤- 5/8(x - 4)² + 10 andy ≥ 0See attached for reference.
hadlee spent 1/4 of her money on christmas presents she had 180 remaining . how much did hadlee soend on christmas present
The amount for handle soend on Christmas present will be 240.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.
Now,
Since, Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.
Let the amount for handle soend on Christmas present = x
Hence, The amount for handle soend on Christmas present will be;
⇒ x - 1/4x = 180
⇒ 3/4x = 180
⇒ 3x = 180 × 4
⇒ 3x = 720
⇒ x = 240
Thus, The amount for handle soend on Christmas present will be 240.
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There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh
graders, and the rest are eighth graders.
How many band members are seventh graders?
Answer:
14
Step-by-step explanation:
10 percent of 70 is 7
20 percent of 70 is 14
So 14 is your answer
Please vote brainliest
Thanks
Have a nice evening
Answer: All you would have to do is multiply 70 by 20% which is 14. So 14 7th graders are a total of the band.
Step-by-step explanation:
Each birthday from age 12, You receive $500. You
save the money in an account that pays an annual yield of 6%. How much money will you
have by the time you're 18?
A cylindrical wooden column is 3 m high and 28 cm in diameter use value π to calculate the mass in kf of the column if the density of the wood is 0.8g/cm^3
Answer:
1.478 kg
Step-by-step explanation:
Considering density=mass/volume, when we rearrange, we get mass=density*volume. Therefore, as we are given the density, we just need to find the volume to know the mass. The volume of a cylinder is πhr^2, and our radius is 28/2=14, so the volume of the cylinder is π*3*14^2=588π. Then, 588π*0.8=470.4π which is about 1477.8052 g. Then, to convert to kg, we can divide this by 1000 and get about 1.478 kg.
suppose that an experimenter studies the lifespan of members of a colony of bacteria. let t be the lifespan of a randomly chosen member of the colony. suppose the lifespan of the bacteria has an exponential distribution with expected value 100 minutes. if we choose 5 members of the colony, what is the probability that at least one of them lives more than 87 minutes?
The probability that at least one of them lives more than 87 minutes is 0.87.
Probability
In statistics, the possible way of happening a particular event is called probability.
Given,
Suppose that an experimenter studies the lifespan of members of a colony of bacteria. let t be the lifespan of a randomly chosen member of the colony. suppose the lifespan of the bacteria has an exponential distribution with expected value 100 minutes.
Here we need to find if we choose 5 members of the colony, then what is the probability that at least one of them lives more than 87 minutes.
Here we know that,
Total number of members = 5
Life span = 87 minutes
Expected value = 100 minutes
So, the probability is calculated as,
=> 87 /100
=> 0.87
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you hold a spherical salad bowl 90 cm in front of your face with the bottom of the bowl facing you. the salad bowl is made of polished metal with a 40 −cm radius of curvature.
By taking out the distance, we know that the image of a 5.0 cm-tall nose is located at 39.29 cm.
What is the distance?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.
The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
So, the equation to be used:
1 / f = 1 / p + 1 / q
The focal length of the metal salad bowl, which behaves like a mirror:
f = R / 2
f = 44/2
f = 22 cm
Suppose that the distance to the item is p = 50 cm, let's find the distance to the image:
1 / q = 1 / f - 1 / p
1 / q = 1/22 - 1/50
1 / q = 0.0254
q = 39.29 cm
Therefore, by taking out the distance, we know that the image of a 5.0 cm-tall nose is located at 39.29 cm.
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Complete question:
You hold a spherical salad bowl 50 cm in front of your face with the bottom of the bowl facing you. The salad bowl is made of polished metal with a 44 cm radius of curvature.
Where is the image of your 5.0-cm-tall nose located?
At the beginning of the year, the number of books owned by a library was 10,000. Since then, it has grown by 1% each month.
Which expressions represent the number of books, in thousands, owned by the library 5 years later if it continues to grow at that rate?
A) 10x ((1+0.01)^12)^5
B) 10x(1+0.01^12) ^60
C) 10x (1.01)^5
D) 10x(1.01)^60
E) 10x (0.01)^60
.
What is the equation of the line that passes through the point (-1,2) and has a slope of -1?
The equation of the line that passes through the point (-1,2) and has a slope of -1, in point-slope form is: y - 2 = -1(x + 1).
What is the Equation of a Line?If we know one point (a, b), that a line passes through and its slope (m), we can write the equation of that line in point-slope form as y - b = m(x - a).
Given the following:
A point (a, b) = (-1, 2)
The slope of the line (m) = -1
To write the equation of the line, substitute m = -1, a = -1, and b = 2 into y - b = m(x - a):
y - 2 = -1(x - (-1))
y - 2 = -1(x + 1).
The answer is: y - 2 = -1(x + 1).
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9. Given that ypı = 3e27 and Ypz = x2 + 3x are particular solutions of y" – 6y' + 5y = -9222 and y" - 6y' + 5y = 5x2 + 3x – 16 respectively, find the particular solutions of a. Y" – 6y + 5y = 5x2 + 3x – 16 – 9223 b. y" – 6y' + 5y = -10x2 - 6x + 32 +622
Particular solution for the equation a. Y" – 6y + 5y = 5x2 + 3x – 16 – 9223 is
5y = -15e²⁷ - 23/5
Particular solution for b. y" – 6y' + 5y = -10x2 - 6x + 32 +622 is 5y = 8x+ 218
Given:
y= 3e²⁷ (Solution 1)
Y = x² + 3x (Solution 2)
y" - 6y' + 5y = -9222 (Equation 1)
y" - 6y' + 5y = 5x² + 3x – 16 (Equation 2)
Where [tex]y^{"}[/tex] represents the double derivative(d²y) of y and [tex]y^{'}[/tex] represents the first derivative(dy) of the equation y.
Find Solutions for:
a. Y" – 6y + 5y = 5x² + 3x – 16 – 9223
b. y" – 6y' + 5y = -10x² - 6x + 32 +622
y= 3e²⁷ (Solution 1)(Given in the question)
Taking derivative on both sides
by = 3 de²⁷
∵ e²⁷ is constant in comparison to dy the derivative will be 0. Thus, d²y of y is also equal to zero
Then, putting values in the equation 1
- 6y' + 5y + y" = -9222 (Equation 1)
(0) - 6(0) +5(3e²⁷) = -9222
Thus, 15e²⁷ = -9222
5e²⁷ = -3074
e²⁷ = -614.8
Y = x² + 3x (Solution 2)(Given in the question)
Taking derivative on both sides
dY/dx= 2x + 3 -(iii)
taking derivative of y'
d²Y/dx² = 2
∵ 3 is a constant in dy/dx.
Then, putting values in the equation 2
y" -+ 5y - 6y' = 5x² + 3x - 16
(2) - 6(2x + 3) +5y = 5x² + 3x - 16 + 12x - 12x
2 - 12 + 18x + 5y = 5x² +15x - 16 -12x
-10 + 18x - 15x + 5y = 5y -16 -12x
3x + 12x =10 - 16
15x = -6
x= -2/5
Putting values of x, y, dy and d²y in equations (i) & (ii)
a. Y" – 6y + 5y = 5x² + 3x - 16 – 9223
(2) -6(2x+3) + 5y = 5x² + 3x - 16 - 9223 + 12x - 12x
2 - 12x -18 + 5y = 5y - 9223 - 16 - 12x
2 + - 18 + 5y -6/5 -(9222 + 1)
2 + 24-6/5 + 5y + 15e²⁷ - 1 = 0
5y + 15e²⁷ + 18/5 + 1= 0
5y + 15e²⁷ + 23/5= 0
5y = -15e²⁷ - 23/5
b. y" – 6y' + 5y = -10x² - 6x + 32 +622
(0) -6(0) + 5y = -10x² - 6x +654
5y = -10x² - 6x -24x + 24x + 654
5y = -10(x² + 3x) +24x + 654
5y = -10y + 24x + 654
5y +10y = 24x + 654
15y=24x+654
5y = 8x+ 218
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a. if you add 2 consecutive counting numbers (such as 47, 48), will the resulting sum always, sometimes, or never be divisible by 2? explain why your answer is true. b. if you add 3 consecutive counting numbers (such as 47, 48, 49), will the resulting sum al-ways, sometimes, or never be divisible by 3? ex-plain why your answer is true. c. if you add 4 consecutive counting numbers (such as 47, 48, 49, 50), will the resulting sum always, sometimes, or never be divisible by 4? explain why your answer is true. d. if you add 5 consecutive counting numbers (such as 47, 48, 49, 50, 51), will the resulting sum always, sometimes, or never be divisible by 5? explain why your answer is true. e. if you add n consecutive counting numbers, will the resulting sum always, sometimes, or never be divisible by n? explain why your answer is true.
On solving the provided question we can say that - the answer is 552 and 558, as consecutive integers.
what is consecutive integers?Consecutive integers are those integers in a computation formula that follow one another. No number is lost in a sequence when enumerating successive numbers, hence their spacing is always consistent. Consecutive integers are the next numbers in ascending order. The consecutive integers formula may be used to discover consecutive integers for any number or to determine if a set of numbers is consecutive or not.
First set the 3 numbers to be x-2, x, and x+2. So:
x-2+x+x+2=554
3x=554
There is no solution to this issue since three cannot split equally into 554. In reality
182+184+186=552
184+186+188=558
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whats 2x3+2 i need serious help
Answer: 8
Step-by-step explanation: Utilizing the POWER of order of operations we will multiply the 2 and 3 together first to get 6 and then add the 2 to get 8. Hope this helped :)
Answer: 8
Step-by-step explanation:
Parenthesis (Please)
Exponent (Excuse)
Multiplication (My)
Division (Dear)
Addition (Aunt)
Subtraction (Sally)
2x3= 6
6+2=8
What are 3 pairs of fractions that have a sum of 5/6. please help
Three pairs of fractions that have a sum of 5/6 are;
1/3 + 2/3 = 5/6
1/4 + 3/4 = 5/6
2/6 + 3/6 = 5/6
How to calculate this?1/3 + 2/3 = 5/6: The fractions have a common bottom number of 3 because they both have the same bottom number.
Adding the top numbers: 1 plus 2 equals 3.
The total is three divided by three, which can also be written as one.
However, we need to show the total with a bottom number of 6 to match the original part. So, we make the top and bottom numbers twice as big to get 2/6. Hence , 1/3 + 2/3 = 2/6.
1/4 + 3/4 = 5/6:The fractions have the same bottom number, so their common denominator is 4.
When you add 1 and 3 together, you get 4.
The sum is four over four, and when simplified, it equals one.
Once again, we have to find a way to write the sum with a bottom number of 6 so that it is the same as the first number in the fraction. So, we take the top number and the bottom number and multiply them both by 3 to get the fraction 3/6. Hence, 1/4 + 3/4 = 3/6.
2/6 + 3/6 = 5/6:In this situation, the fractions already have the same bottom number which is 6.
Adding the top numbers together: 2 + 3 = 5.
The answer is 5/6, which is what we wanted to get.
Therefore each pair shows a different way to add numbers together, either by finding a number that both denominators can divide evenly into or by using numbers that already work well together.
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PLEASE HELP ME WITH THESE 2 QUESTIONS
: Use the following information to find the curvature of each polar curve. For a curve C that is given by the polar equation r ro), the curvature K at the point (, 0) is given by the equation 2(r) (a) r = 1 + sin θ (b) r=θ (c) r=asin θ (d) r=e' Need Help? ReadTalk to a Tutor
On solving the provided question, we can say that - => K not equal to 0 at x= 0 and so, center of curvature exists.
What is center of curvature?In geometry, a curve's center of curvature is located at a point that is offset from the curve by an amount equal to the radius of curvature that lies on the normal vector. zero-curvature point at infinity. The center of the curve serves as the osculating circle. The sphere holding the spherical mirror's center serves as its center of curvature. A "C" is used to symbolize this. the center of a circle with a radius equal to the radius of curvature of a particular point on the curve, whose center is on the concave side of the curve and which is normal to that point.
The curvature K at the point (x,y) is given by if C is a graph of the twice differentiable function y = f(x)y=f(x).
[tex]K = \frac{|y^{''}|}{[1 + (y')^2 ]^{3/2}}[/tex]
Curvature of the given curve at x=0x=0 is
=> K not equal to 0 at x= 0
so,
center of curvature exists.
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solve for x please help asap! will give brainlest
Answer:
80+60+3x+4=180
140+3x+4=180
144+3x=180
3x=180-144
3x=36
x=12
Answer:
x = 12
Step-by-step explanation:
All triangles equal to 180 degrees so, we can set up this expression:
180 = (3x + 4) + 80 + 60
All we have to do is solve:
180 = (3x + 4) + 80 + 60
180 = 3x + 4 + 140
180 = 3x + 144
-144 -144
36 = 3x
/3 /3
12 = x
Which equation has the same solution as 4-2(x-5)=x-19
(A) 2(x+5)= -8.
(B) 3(x-3)=9
(C) x+2=2x-3
(D) 3x-4=2x+7
Answer:
3x-4=2x+7 thus: (D)
x = 11
Step-by-step explanation:
Solve for x:
3 x - 4 = 2 x + 7
Subtract 2 x from both sides:
(3 x - 2 x) - 4 = (2 x - 2 x) + 7
3 x - 2 x = x:
x - 4 = (2 x - 2 x) + 7
2 x - 2 x = 0:
x - 4 = 7
Add 4 to both sides:
x + (4 - 4) = 4 + 7
4 - 4 = 0:
x = 7 + 4
7 + 4 = 11:
Answer: x = 11
___________________________
Solve for x:
4 - 2 (x - 5) = x - 19
-2 (x - 5) = -2 x + 10:
(-2 x + 10) + 4 = x - 19
Add like terms. 4 + 10 = 14:
-2 x + 14 = x - 19
Subtract x from both sides:
(-2 x - x) + 14 = (x - x) - 19
-2 x - x = -3 x:
-3 x + 14 = (x - x) - 19
x - x = 0:
-3 x + 14 = -19
Subtract 14 from both sides:
(14 - 14) - 3 x = -14 - 19
14 - 14 = 0:
-3 x = -14 - 19
-14 - 19 = -33:
-3 x = -33
Divide both sides of -3 x = -33 by -3:
(-3 x)/(-3) = (-33)/(-3)
(-3)/(-3) = 1:
x = (-33)/(-3)
The gcd of -33 and -3 is -3, so (-33)/(-3) = (-3×11)/(-3×1) = (-3)/(-3)×11 = 11:
Answer: x = 11
Answer:3x-4=2x+7
Step-by-step explanation:
first, 4-2x+10=x-19
14+19 =x+2x
33=3x
x=11
A. 2x+10=8
2x= -18
x=-9
B. 3x-9=9
3x=18
x=6
C. x+2=2x-3
3x = 5
x = 5/3
D. 3x-4 = 2x+7
3x-2x=7+4
x=11
Supply the missing information for each of the right triangles described below. In each example, θ = angle, O = opposite side, A = adjacent side, and H = hypotenuse.
Choice 'A' H = 54.93
Choice 'B' H ≈ 5.493
Choice 'C' H = 5.493
Choice 'D' H ≈ 54.93
Each right triangle has a missing value of 1.9096 where = angle, O = opposing side, A = adjacent side, and H = hypotenuse.
what is right triangle ?A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangle triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
given,
1.9096 is what's lacking.
SOH CAH TOA's identification would appear to be:
The opposite or hypotenuse of sin
Sinθ = O/H
the following being spoken
H = 11 \sin θ = 0.1736
To replace having, use:
0.1736 = O/11
O = 11 * 0.1736
O = 1.9096
the missing value is 1.9096.
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What is the equation of the line that passes through the point (-3,-3)(−3,−3) and has a slope of 33?
The required equation of the line having a slope of 33 and passing through (-3, - 3) is y = 33x + 96.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Let the required line be y = mx + b.
∴ - 3 = (33)(-3) + b.
- 3 = - 99 + b.
b = 96.
∴ y = 33x + 96 is the required line.
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Grocery Store A is selling bananas for $0.75 for 12 pound. Grocery Store B is selling 5 pounds of bananas for $3.75. Which store is offering the best unit rate?
Store B is offering the best unit rate for bananas.
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
Grocery Store A is selling bananas for $0.75 for 12 pounds.
The unit rate will be = 0.75/12 = 0.06
Grocery Store B is selling 5 pounds of bananas for $3.75.
The unit rate will be = 3.75/5 = 0.75
Hence, Store B is offering the best unit rate for bananas.
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lorenzo is a kickboxing instructor who will be teaching classes at a local gym. to get certified as an instructor, he spent a total of $94. lorenzo will be earning a base salary of $79 per month from the gym, plus an additional $3 for every class he teaches. if lorenzo teaches a certain number of classes during his first month as an instructor, he will earn back the amount he spent on certification. how many classes will that take? how much will lorenzo's expenses and earnings be?
Lorenzo will take 4 classes total in first month. Also, his expense will be $15 and earning will be $79.
Given that:
Amount he spends = $94
His base salary = $79/ month
Additional amount = $ 3
Let x represents the money he earn for every one class.
we can no put it in a equation:
79(1) + 3x = 94
⇒ 79 +3x = 94
⇒ 3x = 15
⇒ x = 15/3
⇒ x = 5
Therefore, Lorenzo will take 4 classes total in first month. Also, his expense will be $15 and earning will be $79.
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At what annual percent rate would you need to invest $12,000 and make $2,880 in interest after 8 years?
Use your calculator to evaluate a¯=−3.7meter/second−13.9meter/second21.4second−7.2second. Part A Average acceleration Use your calculator to evaluate -3.7 meter/second-13.9 meter/second 21.4 second-72…
The average acceleration is - 1.24 m/s². The result is calculated by using calculator. See the picture in the attachment!
What is average acceleration?Average acceleration is the rate of change in velocity per unit time. The formula can be expressed as
[tex]\overline{a} = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex]
Where
v₂ = final velocityv₁ = initial velocityt₂ = final timet₁ = initial timeCalculate this average acceleration using calculator!
[tex]\overline{a} = \frac{-3.7 \: m/s \: - 13.9 \: m/s}{21.4 \: s- 7.2 \: s}[/tex]
See the picture in the attachment!
The average acceleration after rounding is
[tex]\overline{a} = -1.23943661972 \: m/s \: /s[/tex]
[tex]\overline{a} = -1.24 \: m/s^{2}[/tex]
Hence, the average acceleration from the data is - 1.24 m/s².
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