Answer:
14 cm
Step-by-step explanation:
If the rectangle is 15 cm wide then the total width is 30.
So we can subtract 30 from 70,
=40
If the length is increased by 2 then there is 4 more cm added to the total length.
We can do, 40-4
=38
If 38 is the total length we do 38 ÷ 2
=14
Thus,
The original length was 14 cm.
Answer:
18cm
Step-by-step explanation:
We can set up an equation to solve this
Let's start by naming the original length before the increase x.
New length is x+2.
Formula for perimeter of a rectangle is 2L+2W=P
Plug known values in
2(x+2)+2(15)=70
Simplify
2x+4+30=70
2x+34=70
2x=36
x=18
The original length is 18cm.
Does the following systems produce an infinite number of solutions 2y + x = 4 ; 2y = -x +4
Answer:
Yes.
Step-by-step explanation:
In the future, simply plug both equations into Desmos.
In 12 years, a bond with a 6.35% annual rate earned $7620 as simple interest. What was the principle amount of the bond
Answer:
The principal amount is $10160
Step-by-step explanation:
Given; Simple interest, I = 7620
Rate, R = 6.25
Time, T = 12
Principal, P =?
The formula for simple interest, I is;
[tex]I = \frac{PRT}{100}[/tex]
Making P the subject of formula;
[tex]P = \frac{I100}{RT}[/tex]
[tex]P = \frac{7620 *100}{6.25*12}[/tex]
[tex]P = \frac{762000}{75}\\P = 10160[/tex]
Therefore, the principal amount is $10160
Answer:
10000
Step-by-step explanation:
If an amount of money, P, called the principal, is invested for a period of t years at an annual interest rate r, the amount of simple interest, I, earned is given by
I=PrtwhereIPrt=interest=principal=rate=time
The following information is given.
Irt=$7,620=0.0635=12 years
Substituting the given information into the simple interest formula and solving for P gives
7,6207,620=(P)(0.0635)(12)=0.762P
Dividing both sides by 0.762, we have
P=7,6200.762=10,000
Thus, the principal amount of the bond was $10,000.
which number should.be added to the data so that the range of the data is 31? 54,72,64,57
Answer: 41 or 85
Step-by-step explanation:
Range is the difference between the largest number and the smallest number.
The largest number is 72. 72 - 31 = 41
The smallest number is 54. 54 + 31 = 85
Adding either ONE of those numbers will result in a range of 31.
pls pls help me help me help me
Answer:
2
Step-by-step explanation:
Answer:
I hope it will help you....
Lagrange's four-square theorem states that every positive integer can be written as the sum of four or
fewer square numbers. For instance, 23 - 32+32 +22+12 and 30 -5° +2° +1°. Write each
of the following integers as the sum of four or fewer square numbers.
a. 15
b. 24
0.33
d. any 3-digit, positive integer of your choosing
Answer:
15 = 3² +2² +1² +1²24 = 4² +2² +2²33 = 4² +4² +1²624 = 22² +10² +6² +2²Step-by-step explanation:
It doesn't always work to choose the largest possible square first.
a. 15 = 9 + 4 + 1 + 1 = 3² +2² +1² +1²
b. 24 = 16 + 4 + 4 = 4² +2² +2²
c. 33 = 25 + 4 + 4 = 5² +2² +2²
d. 624 = 484 +100 +36 +4 = 22² +10² +6² +2²
Using π = 3.14, find the area of a circle with a radius of 4.2. Round your answer to the nearest hundredth. will give brainliest
Answer:
55.39 units ^2Step-by-step explanation:
A=pi*r^2
A=3.14*4.2^2
A=3.14*17.64
A=55.3896
A≈55.39 units ^2
Answer:
55.42
Step-by-step explanation:
So since we know that how you calculate a circle's area is the formula -->
π (r)^2 (r is radius), We can simply just plug all the numbers in -->
3.14 (4.2)^2 => 4.2 squared is 17.64 => 3.14 (17.64) = around 55.417 but since we want to round it to the nearest hundred, we get 55.42
Hope this helps!
I NEED HELP PLEASE ASAP! :)
Anne is pushing a wheelbarrow filled with mulch to place in her garden. She is pushing the wheelbarrow with a force of 70 N at an angle of 50° with the horizontal. How much work in joules is Anne doing when she pushes the wheelbarrow 25 meters? (Show work)
Answer:
See below.
Step-by-step explanation:
Again, another great question!
This should be under physics, as it involves Work = Force * Distance. As Anne pushes the wheelbarrow with a force of 70 Newtons with respect to an angle of 50 degrees horizontal, the horizontal force is 70( cos 50 ). The distance over which the work is done is 25 meters, so work should be -
Work = ( 70( cos 50 ) )( 25 ),
Work = ( About ) 1124.87 Joules
The work done when Anne pushes the wheelbarrow a distance of 25 meters, is 1124.87 Joules
Show all work to solve 3x^2 – 5x – 2 = 0.
Answer:
Step-by-step explanation:
3x2−5x−2=0
For this equation: a=3, b=-5, c=-2
3x2+−5x+−2=0
Step 1: Use quadratic formula with a=3, b=-5, c=-2.
x= (−b±√b2−4ac )2a
x= (−(−5)±√(−5)2−4(3)(−2) )/2(3)
x= (5±√49 )/6
x=2 or x= −1 /3
Answer:
x=2 or x= −1/ 3
The solutions to the equation are x = -1/3 and x = 2.
Here are the steps on how to solve [tex]3x^{2}[/tex] – 5x – 2 = 0:
First, we need to factor the polynomial. The factors of 3 are 1, 3, and the factors of -2 are -1, 2. The coefficient on the x term is -5, so we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Next, we set each factor equal to 0 and solve for x.
(3x + 1)(x - 2) = 0
3x + 1 = 0
3x = -1
x = -1/3
x - 2 = 0
x = 2
Therefore, the solutions to the equation [tex]3x^{2}[/tex] – 5x – 2 = 0 are x = -1/3 and x = 2.
Here is the explanation for each of the steps:
Step 1: In order to factor the polynomial, we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Step 2: We set each factor equal to 0 and solve for x. When we set 3x + 1 equal to 0, we get x = -1/3. When we set x - 2 equal to 0, we get x = 2. Therefore, the solutions to the equation are x = -1/3 and x = 2.
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I NEED HELP PLEASE, THANKS! :)
A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, the second row has 24 seats, the third row has 32 seats, and so on, increasing by 8 seats each row for a total of 50 rows. Find the number of people that can be accommodated in the sixteenth row. (Show work)
Answer: 136
Step-by-step explanation:
An= A1+(n-1)d
A1=16, d=8, and n=16
A16= 16 +(16-1)(8)
A16= 16(15)(8)
A16= 16+120
A16=136
Hey there! :)
Answer:
f(16) = 136 seats.
Step-by-step explanation:
This situation can be expressed as an explicit function where 'n' is the row number.
The question also states that the number of seats increases by 8. Use this in the equation:
f(n) = 16 + 8(n-1)
Solve for the number of seats in the 16th row by plugging in 16 for n:
f(16) = 16 + 8(16-1)
f(16) = 16 + 8(15)
f(16) = 16 + 120
f(16) = 136 seats.
Amit solved the equation StartFraction 5 over 12 EndFraction = Negative StartFraction x over 420 EndFraction for x using the steps shown below. What was Amit’s error?
Answer:
The product of 5/ 12 and –420 should have been the value of x.
Answer: D
Step-by-step explanation:
Took the test
A rectangular park measuring 32 yards by 24 yards is surrounded by a trail of uniform width. If the area of the park and the trail combine is 1748 square yards, what is the width of the park
Answer:
The width = 38 yard
Step-by-step explanation:
Given
Dimension of Park = 32 by 24 yard
Area = 1748 yd²
Required
Find the width of the park
Given that the park is surrounded by a trail;
Let the distance between the park and the trail be represented with y;
Such that, the dimension of the park becomes (32 + y + y) by (24 + y + y) because it is surrounded on all sides
Area of rectangle is calculated as thus;
Area = Length * Width
Substitute 1748 for area; 32 + 2y and 24 + 2y for length and width
The formula becomes
[tex]1748 = (32 + 2y) * (24 +2y)[/tex]
Open Bracket
[tex]1748 = 32(24 + 2y) + 2y(24 + 2y)[/tex]
[tex]1748 = 768 + 64y + 48y + 4y^2[/tex]
[tex]1748 = 768 + 112y + 4y^2[/tex]
Subtract 1748 from both sides
[tex]1748 -1748 = 768 -1748 + 112y + 4y^2[/tex]
[tex]0 = 768 -1748 + 112y + 4y^2[/tex]
[tex]0 = -980 + 112y + 4y^2[/tex]
Rearrange
[tex]4y^2 + 112y -980 = 0[/tex]
Divide through by 4
[tex]y^2 + 28y - 245 = 0[/tex]
Expand
[tex]y^2 + 35y -7y - 245 = 0[/tex]
Factorize
[tex]y(y+35) - 7(y + 35) = 0[/tex]
[tex](y-7)(y+35) = 0[/tex]
Split the above into two
[tex]y - 7 = 0\ or\ y + 35 = 0[/tex]
[tex]y = 7\ or\ y = -35[/tex]
But y can't be less than 0;
[tex]So,\ y = 7[/tex]
Recall that the dimension of the park is 32 + 2y by 24 + 2y
So, the dimension becomes 32 + 2*7 by 24 + 2*7
Dimension = 32 + 14 yard by 24 + 14 yard
Dimension = 46 yard by 38 yard
Hence, the width = 38 yard
Question 65
Find area of figure. Round to the nearest hundredth if necessary.
rectangle with circle taken out
5.0 m
10.4 m
(Use 3.1 4 for a.)
Answer:
32.38 square m
Step-by-step explanation:
Diameter of semicircle = 5 m
Hence, radius = 5/2 = 2.5 m
Area of figure = Area of rectangle - 2 times area of one semicircle
[tex] = l \times b - 2 \times \frac{1}{2} \pi {r}^{2} \\ \\ = 10.4 \times 5 - \pi {r}^{2} \\ = 52 - 3.14 \times {(2.5)}^{2} \\ = 52 - 3.14 \times 6.25 \\ = 52 - 19.625 \\ = 32.375 \\ \approx 32.38 \: {m}^{2} \\ [/tex]
What are the zeros of the quadratic function f(x) = 6x² + 12x – 7?
x = -1
ve
13
6
and x = -1 +
13
V6
X = -1
2
V3
2
and x = -1 +
V3
X = -1
and x = -1 +
+
7
V 6
6
1
x = -1
1
16
and x = -1 +
V6
Answer:
x = -2.47, 0.47
Step-by-step explanation:
Easiest and quickest way to do this is to graph the quadratic and analyze for x-intercepts.
Alternatively, we have to use the Quadratic Formula because we cannot factor the expression.
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = ln 5x, y = 2, y = 3, x = 0; about the y-axis
2.Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y2 = 2x, x = 2y; about the y-axis
3.Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = x, y = 0, x = 2, x = 7; about x = 1
Answer:
1. V = 15.95 (to 2 decimal places)
2. V = 107.23 (to 2 decimal places)
3. V = 560.25 (to 2 decimal places)
Step-by-step explanation:
1. y = ln 5x, y = 2, y = 3, x = 0; about the y-axis
Find volume using the disk method.
First find inverse of y=ln(5x)
5x = exp(y)
x(y)=exp(y)/5
Width of each strip = dy
length of each strip = x(y)
volume of each disk by rotation of strip about y=axis
dV = 2*pi*x(y)dy
total volume
V = integral (dV) for y=2 to 3
= integral (2*pi*e^y/5) for y=2 to 3
= 2*pi*(e^y/5) for y=2 to 3
= 2pi(e^3-e^2)/5
= 15.95 (to 2 decimal places)
2. y2 = 2x, x = 2y; about the y-axis
Find point of intersection between
solve y^2/2 = 2y => y=4, x=2y=8, therefore
intersection is at (8,4), which is the upper integration limit
Using the disk method again
Volume of each disk
dV(y) = pi((2y)^2-(y^2/2)^2)dy
Total volume of solid
V = integral(pi((2y)^2-(y^2/2)^2)dy) for y=0 to 4
= pi (4y^3/3 - y^5/20) for y = 0,4
= pi (256/3 - 1024/20)
= 512pi/15
= 107.23 (to 2 decimal places)
3. y = x, y = 0, x = 2, x = 7; about x = 1
Use the shell method.
volume of each shell formed by roatation of a vertical strip about the axis of rotation (x=1)
dV = 2*pi*(x-1)*(y*dx)
Total volume of rotation
V = integral(2*pi*(x-1)*y dx for x=2 to 7
= 535pi/3
= 560.25 (to 2 decimal places)
I NEED HELP PLEASE, THANKS! :)
Answer:
-0.4
Step-by-step explanation:
Since x=4 is not a critical point, you can simply evaluate the function. You can do this in your head.
(2√4 -6)/(9 -4) = (2·2 -6)/5 = -2/5 = -0.4
A kite 100 feet above the ground is being blown away from the person holding its string in a direction parallel to the ground at a rate of 10 feet per second. At what rate must the string be let out when the length of string already let out is 200 feet? (Hint: start by drawing a picture. There should be a triangle involved.) You need not simplify your answer.
Answer:
5√3 ft/s
Step-by-step explanation:
Let h represent the horizontal distance of the kite from the person. Let s represent the string length. Then the Pythagorean theorem tells us ...
s^2 = 100^2 + h^2
2s·ds/dt = 0 + 2h·dh/dt
ds/dt = (h/s)·dh/dt
So, we need to know the horizontal distance when s=200.
200^2 = 100^2 + h^2
40000 -10000 = h^2
h = 100√3
Substituting known values into the equation for ds/dt, we have ...
ds/dt = (100√3)/(200)(10 ft/s) = 5√3 ft/s
The string must be let out at 5√3 ft/s when it is already 200 ft long.
Need help with this as soon as possible
Answer:
Step-by-step explanation:
[tex]\frac{14}{x} =14/x[/tex]
Thus, we can multiply both sides by x to get 14=0. Because 14 does not equal 0, the equation has no solutions. A value of x that makes the equation false is 541, which makes the simplified equation turn into 14=0.
Another value of x that makes the equation false is 7, which makes the simplified equation turn into 14=0.
Hope it helps <3
A high school track team has a grade point average of 3.36, with a standard deviation of 1.2. Their coach wants to identify the team members in the bottom 33% for extra tutoring help. What is the grade point average that will mean that a track team athlete will be recommended for extra tutoring help if the coach examines just 32 of her athletes
Answer:
GPAs os 2.832 and lower will mean that a track team athlete will be recommended for extra tutoring help
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 3.36, \sigma = 1.2[/tex]
Bottom 33%:
The 33rd percentile(X when Z has a pvalue of 0.33) and below.
So we have to find X when Z = -0.44.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.44 = \frac{X - 3.36}{1.2}[/tex]
[tex]X - 3.36 = -0.44*1.2[/tex]
[tex]X = 2.832[/tex]
GPAs os 2.832 and lower will mean that a track team athlete will be recommended for extra tutoring help
Consider a spinner numbered 1-7. You find that the probability of getting an even number is and the probability of getting an odd number is.
Which rule of probability could you use to find the probability of getting an even number OR an odd number?
Difference Rule
O
Product Rule
Sum Rule
O
Quotient
The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Find a linear function that approximates the number of products sold as a function of the cost of advertising. Select the most appropriate answer. cost = 9 2 3 4 2 5 9 10 and number 85 52 55 68 57 86 83 73
Options :
(A.) y=558-273x (B.) y=264+142x (C.) y = 55.8 +2.79x (D.) y= -26.4-1.42x
Answer:
C.) ŷ = 2.79X + 55.8
Step-by-step explanation:
Given the data:
cost (x): 9 2 3 4 2 5 9 10
Number of products sold: 85 52 55 68 57 86 83 73
Using the online regression calculator to generate a linear regression plot of the given data: the model obtained is given below
ŷ = 2.79X + 55.8
With y being the predicted or dependent variable
Slope or gradient of the line = 2.79
X = the independent variable
55.8 = the intercept.
Graph the exponential model y = 3(6)x .Which point lies on the graph?
Answer:
0
Step-by-step explanation:
y = 3 × 6x
0 = 3 × 6x
0 = 18x
18x = 0
x = 0
Hope this helps! :)
A tablet contains 0.5 mg of medication. A patient receives 5 tablets a day. How many mg patient receive per day?
Answer:
2.5 mg
Step-by-step explanation:
.5 x 5 = 2.5
Find the product. (a - 8)(a + 2) A. 2a - 6 B. a2 - 16 C. a2 - 10a + 16 D. a2 - 6a - 16
Answer:
D. a^2 - 6a - 16
Step-by-step explanation:
The product is found using the distributive property.
(a -8)(a +2) = a(a +2) -8(a +2)
= a^2 +2a -8a -16
= a^2 -6a -16 . . . . . matches choice D
which term is the rate at which work is done
Answer:
The answer is power.Hope this helps you
HELP ASAP! The number of entertainment websites in 1995 wass 54. By 2004 there were 793 entertainment website..
Approximately, what was the rate of change for the number of the websites for this time period??
=============================================================
How I got that answer:
We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.
Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.
----------
You could use the slope formula to get the job done. This is because the slope represents the rise over run
slope = rise/run
The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...
In a more written out way, the steps would be
slope = rise/run
slope = (y2-y1)/(x2-x1)
slope = (793 - 54)/(2004 - 1995)
slope = 739/9
slope = 82.111....
The manager of a mall conducted a survey among two groups (n1 = 100, n2 = 100) of visitors to the mall on different days. She found that the first group spent an average of 60 minutes in the mall, while the second group spent an average of 90 minutes in the mall. If the manager wishes to see the difference in the average times spent by the two groups in the mall,
Which of the following could be the alternative hypothesis?
a. The difference in the average times spent by the two groups in the mall is 30 minutes.
b. There is at least some difference in the average times spent by the two groups in the mall.
c. There is a difference in the average times spent by the two groups in the mall, with a standard deviation of 30 minutes.
d. There is no difference in the average times spent by the two groups in the mall.
Answer:
Option B - There is at least some difference in the average times spent by the two groups in the mall.
Step-by-step explanation:
A null hypothesis is a hypothesis that states that there is no statistical significance between the two variables. Thus, It is usually the hypothesis that a researcher or experimenter will try to disprove or discredit. While an alternative hypothesis is one that states there is a statistically significant relationship between two variables.
Now, applying these definitions to the question, we can see that;
Null Hypothesis is;
H0; There is no difference in the average times spent by the two groups in the mall
While the alternative hypothesis is;
Ha; There is at least some difference in the average times spent by the two groups in the mall
Thus, correct answer is option B
Answer:
It is option b
Step-by-step explanation:
? QUESTION
Write 5.25% as a fraction in simplest form.
Answer:
5 1/4
Step-by-step explanation:
5 is the whole number so we up it aside.
Then we are left with 25/100,when we simplify that 25 into 25 is 1.
25 into 100 is 4 times.
Therefore we are left with 1/4.
I hope this helps :)
Answer:
5 1/4 because 1/4=25 and not only that u could do 5 25/100 and simplfy and u get 5 1/4
Step-by-step explanation:
Write the improper fraction as a mixed number 29/5
Answer:
5 4/5
Step-by-step explanation:
29 ÷ 5 = 5
29 - 25 = 4
Since 5x5 is 25 and we have 4 as a remainder we put it over the original denominator 5.
I really hope this helps.
29/5 as a mixed number is 5 and 4/5.
To convert the indecorous bit29/5 into a mixed number.
First, divide the numerator( 29) by the denominator( 5) and express the result as a whole number and a bit.
Now, 29 divided by 5 equals 5 with a remainder of 4.
The quotient( 5) becomes the whole number part of the mixed number, and the remainder( 4) becomes the numerator of the bit part, while the denominator remains the same.
Thus, 29/5 as a mixed number is 5 and 4/5.
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[tex]\frac{d}{7}[/tex] + –59 = –50
d = _______
An urn contains 4 white balls and 7 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 11 balls: (a) If 2 balls are white and 1 is red? (b) If all 3 balls are white? (c) If all 3 balls are red?
Answer:
(a) 2 white & 1 red ball = 42 ways
(b) All 3 white balls = 4 ways
(c) All 3 red balls = 35 ways
Step-by-step explanation:
An urn contains 4 white balls and 7 red balls. Three balls are selected.
In how many ways can the 3 balls be drawn from a total of 11 balls:
(a) If 2 balls are white and 1 is red?
The 2 white balls can be selected in ⁴C₂ ways
The 1 red ball can be selected in ⁷C₁ ways
2 white & 1 red ball = ⁴C₂ × ⁷C₁
2 white & 1 red ball = 6 × 7
2 white & 1 red ball = 42 ways
(b) If all 3 balls are white?
The 3 white balls can be selected in ⁴C₃ ways
The 0 red ball can be selected in ⁷C₀ ways
All 3 white balls = ⁴C₃ × ⁷C₀
All 3 white balls = 4 × 1
All 3 white balls = 4 ways
(c) If all 3 balls are red?
The 3 red balls can be selected in ⁷C₃ ways
The 0 white ball can be selected in ⁴C₀ ways
All 3 red balls = ⁷C₃ × ⁴C₀
All 3 red balls = 35 × 1
All 3 red balls = 35 ways