Answer:
[tex]Area =24cm^2[/tex]
Step-by-step explanation:
Given
[tex]L = 8cm[/tex]
[tex]W = 12cm[/tex]
[tex]r = 2[/tex] -- folded twice
Required
The area of the new rectangle
When the length was folder, the new length is:
[tex]l = L/2 = 8cm/2 = 4cm[/tex]
When the width was folder, the new width is:
[tex]w = W/2 = 12cm/2 = 6cm[/tex]
So, the new area is:
[tex]Area =l * w[/tex]
[tex]Area =4cm * 6cm[/tex]
[tex]Area =24cm^2[/tex]
Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate the derivative when x = 5 mm.
V'(5) = mm3/mm
What does V'(5) mean in this situation?
Answer:
I don't know the answer it is to hard.
In the figure, m is parallel to n and m <4 = 125 degrees. Find the measures of the other angles.
Answer:
m<1 = 55°
m<2 = 125°
m<3 = 55°
m<5 = 55°
m<6 = 125°
m<7 = 55°
m<8 = 125°
Step-by-step explanation:
m<4 = 125° (given)
✔️m<8 = m<4 (alternate exterior angles are congruent)
m<8 = 125° (substitution)
✔️m<1 = 180° - m<8 (supplementary angles/linear pair)
m<1 = 180° - 125° (substitution)
m<1 = 55°
✔️m<2 = m<8 (vertical angles are congruent)
m<2 = 125° (substitution)
✔️m<7 = m<1 (vertical angles are congruent)
m<7 = 55° (Substitution)
✔️m<3 = m<7 (alternate interior angles are congruent)
m<3 = 55° (substitution)
✔️m<5 = m<3 (vertical angles are congruent)
m<5 = 55°
✔️m<6 = m<4 (vertical angles)
m<6 = 125°
18 is 65% of what number
Answer:
65% of 27.69 is 18.
Step-by-step explanation:
Formula = Number x 100
Percent = 18 x 100
65 = 27.69
Following shows the steps on how to derive this formula
Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.
18
65% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
65Y = 18 x 100
65Y = 1800
Y = 1800
100 = 27.69
Identify the X intercept and the yIntercept of the line 4x-2y=-12
Answer:
X-intercept = -3 and y-intercept = 6
Step-by-step explanation:
We can start off by isolating the y term. To do that, we must add 2y to both sides to get
[tex]4x=2y-12[/tex]
Now, we must add 12 to both sides and the y term will be all alone on the right side:
[tex]4x+12=2y[/tex]
Now, to have only y on the right side, we must divide by 2 to get:
[tex]y=2x+6[/tex]
In slope-intercept form, b is the y-intercept, and 'b' in this equation is 6. We have our y-intercept.
To find our x-intercept, y must be equal to zero. We can plug in that value for y and solve for x:
[tex]0=2x+6[/tex]
We can start off by subtracting 6 from both sides to get:
[tex]2x=-6[/tex]
We can then divide both sides to get [tex]x=-3[/tex] when y is equal to 0. Thus, we have our x-intercept.
Answer:
y-intercept= -6
x-intercept= 3
Step-by-step explanation:
First, rearrange the equation to be in y=mx+b.
4x-2y=12
4x-12=2y
(1/2)(4x-12)=y
y=2x-6
From here, we know that the 'b' in an equation in form y=mx+b is the y-intercept, which is -6.
To find the x intercept make y=0 and solve.
You can also solve without rearranging the equation and simply making x=0 and solving to find the y-intercept. and making y=0 and solving to find the x-intercept.
Which one is the intersection point of
f(x) = x3 + 3x and
g(x) = x2 + 3
A) (0,0)
B) (0,3)
C) (1,4)
D) (-1,4)
I URGENTLY NEED HELP PLEASE , I WOULD ALSO MARK AS BRAINLIEST!!
Answer: C) (1,4)
Step-by-step explanation:
The intersection point is where f(x) = g(x)
x³ + 3x = x² + 3
x³ - x² +3x - 3 = 0
A. (0, 0) → x = 0 → (0)³ - (0)² +3(0) - 3 = -3 ≠ 0B. (0, 3) → x = 0 → (0)³ - (0)² +3(0) - 3 = -3 ≠ 0C. (1, 4) → x = 1 → (1)³ - (1)² +3(1) - 3 = 0 + 0 = 0D. (-1, 4) → x = -1 → (-1)³ - (-1)² +3(-1) - 3 = 0 - 3 - 3 = -6 ≠ 0Question 5 plz show steps
Answer:
C
Step-by-step explanation:
Find the area of a triangle as a mixed number.
Answer:
I believe the answer is 4 37/50!
The height of a projectile fired upward is given by the formula
s = v0t − 16t2,
where s is the height in feet,
v0
is the initial velocity, and t is the time in seconds. Find the time for a projectile to reach a height of 96 ft if it has an initial velocity of 128 ft/s. Round to the nearest hundredth of a second.
Answer:
The projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.
Step-by-step explanation:
The height of a projectile fired upward is given by the formula:
[tex]\displaystyle s = v_{0} t - 16t^2[/tex]
Where s is the height in feet, v₀ is the initial velocity, and t is the time in seconds.
Given a projectile with an initial velocity of 128 ft/s, we want to determine how long it will take the projectile to reach a height of 96 feet.
In other words, given that v₀ = 128, find t such that s = 96.
Substitute:
[tex](96) = (128)t-16t^2[/tex]
This is a quadratic. First, we can divide both sides by -16:
[tex]-6 = -8t+t^2[/tex]
Isolate the equation:
[tex]t^2 - 8t + 6 = 0[/tex]
The equation isn't factorable, so we can consider using the quadratic formula:
[tex]\displaystyle t = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
In this case, a = 1, b = -8, and c = 6. Substitute:
[tex]\displaystyle t = \frac{-(-8)\pm\sqrt{(-8)^2-4(1)(6)}}{2(1)}[/tex]
Simplify:
[tex]\displaystyle t = \frac{8\pm\sqrt{40}}{2} = \frac{8\pm 2\sqrt{10}}{2} = 4\pm \sqrt{10}[/tex]
Hence, our two solutions are:
[tex]\displaystyle t = 4+\sqrt{10} \approx 7.16\text{ or } t= 4-\sqrt{10} \approx 0.84[/tex]
So, the projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.
(1 point) There were 23.7 million licensed drivers in California in 2009 and 22.76 million in 2004. Find a formula for the number, N, of licensed drivers in the US as a function of t, the number of years since 2004, assuming growth is (a) Linear N(t)
Answer:
N(t) = 0.188t + 22.76
Step-by-step explanation:
Number of licensed drivers in 2004 = 22.76 million
Number of licensed drivers in 2009 = 23.7 million
Number of licensed drivers, N as a function of t since year 2004 ;
General form of a linear function :
y = mx + c
c = intercept ; m = slope
Intercept c = value of y ; when x = 0
Here, population after uerssmmx,
Hence,
In 2004 ;
22.76 = mx + c
x = 0
22.76 = c
Number in 2009
x = number of yesrs after 2004 ; x = 2000 - 2004 = 5years
We can find the slope :
y = m*5 + 22.76
y = 23.7 in 2009
23.7 = 5m + 22.76
23.7 - 22.76 = 5m
m = 0.94 / 5
m = 0.188
Hence, the linear function can be written as :
N(t) = 0.188t + 22.76
Two equal positive charges are placed x m apart. The equipotential lines are at 100 V interval. The work required to move a third charge, q = -e, from the +100 V line to b is:______
Answer:
+200 J
Step-by-step explanation:
The equally positive charges plates are placed at point x. Exponential lines are 100 V interval and therefore the charges on the potential line is positive. The potential for line c is +200 V which indicates that work required to move the third line is +200 J.
Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have following salaries (in $1000s): 70, 80, 90. The average and the standard deviation of the data in the sample are 80 and 10. Using hypothesis testing, determine if this sample provides a sufficient evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $60,000.
a. Null hypothesis.
b. alternative hypothesis.
c. test statistic.
d. acceptance region.
Answer:
H0 : μ = 60000
H1 : μ ≠ 60000
Test statistic = 3.464
Step-by-step explanation:
Given :
Sample mean salary, xbar = 80000
Sample standard deviation, s = 10000
Population mean salary , μ = 60000
Sample size, n = 3
Hypothesis :
H0 : μ = 60000
H1 : μ ≠ 60000
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (80000 - 60000) ÷ (10000/√(3))
T = 20000 / 5773.5026
T = 3.464
The Decison region :
If Tstatistic >Tcritical
Tcritical at 10%, df = 2 ; two - tailed = 2.9199
Tstatistic > Tcritical ; He
A dinner mint costs 85¢ and a toffee costs 73¢. What is the cost of both sweets rounded to the nearest dollar?
Answer:
85 rounded to the nearest dollar would be $1. 73 rounded to the nearest dollar would also be $1
Step-by-step explanation:
Determine the product of (46.2 × 10^-1) ⋅ (5.7 × 10^–6). Write your answer in scientific notation.
A)
2633.4 × 10^–5
B)
2.6334 × 10^–7
C)
2.6334 × 10^–1
D)
2.6334 × 10^–5
Step-by-step explanation:
here's the answer to your question
Nadia is ordering cheesecake at a restaurant, and the server tells her that she can have up to five toppings: caramel, whipped cream, butterscotch sauce, strawberries, and hot fudge. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge
Answer:
The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P = 1/32 = 0.03125
Step-by-step explanation:
There are up to 5 toppings, such that the toppings are:
caramel
whipped cream
butterscotch sauce
strawberries
hot fudge
We want to find the probability that, If the server randomly chooses which toppings to add, she gets just caramel, butterscotch sauce, strawberries, and hot fudge.
First, we need to find the total number of possible combinations.
let's separate them in number of toppings.
0 toppins:
Here is one combination.
1 topping:
here we have one topping and 5 options, so there are 5 different combinations of 1 topping.
2 toppings.
Assuming that each topping can be used only once, for the first topping we have 5 options.
And for the second topping we have 4 options (because one is already used)
The total number of combinations is equal to the product between the number of options for each topping, so here we have:
c = 4*5 = 20 combinations.
But we are counting the permutations, which is equal to n! (where n is the number of toppings, in this case is n = 2), this means that we are differentiating in the case where the first topping is caramel and the second is whipped cream, and the case where the first topping is whipped cream and the second is caramel, to avoid this, we should divide by the number of permutations.
Then the number of different combinations is:
c' = 20/2! = 10
3 toppings.
similarly to the previous case.
for the first topping there are 5 options
for the second there are 4 options
for the third there are 3 options
the total number of different combinations is:
c' = (5*4*3)/(3!) = (5*4*3)/(3*2) = 10
4 toppings:
We can think of this as "the topping that we do not use", so there are only 5 possible toppings to not use, then there are 5 different combinations with 4 toppings.
5 toppings:
Similar to the first case, here is only one combination with 5 toppings.
So the total number of different combinations is:
C = 1 + 5 + 10 + 10 + 5 + 1 = 32
There are 32 different combinations.
And we want to find the probability of getting one particular combination (all of them have the same probability)
Then the probability is the quotient between one and the total number of different combinations.
p = 1/32
The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P = 1/32 = 0.03125
Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week. A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 35 students studied each week was 21.1 hours. The sample standard deviation of 4.3 hours.
Find the p-value.
The p-value should be rounded to 4-decimal places.
Answer:
0.0698
Step-by-step explanation:
Given :
Population mean, μ = 20
Sample mean, xbar = 21.1
Sample standard deviation, s = 4.3
Sample size, n = 35
The hypothesis :
H0 : μ = 20
H0 : μ > 20
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (21.1 - 20) ÷ (4.3/√(35))
T = 1.1 ÷ 0.7268326
Test statistic = 1.513
Using the Pvalue calculator :
df = n - 1 = 35 - 1 = 34
Pvalue(1.513, 34) = 0.06976
Pvalue = 0.0698 (4 decimal places)
The p-value is 0.0698 if rounded to 4-decimal places.
It is given that students study an average of more than 20 hours each week and the random sample of 35 students was asked to keep a diary of their activities over a period of several weeks.
The average number of hours that the 35 students was 21.1 hours.
The sample standard deviation is 4.3 hours.
It is required to find the p-value.
What is the standard deviation?It is defined as the measure of data dispersement, It gives an idea about how much is the data spread out.
We can test the hypothesis using the Z test, the formula for the Z-test is given below:
[tex]\rm Z= \frac{(x-u)}{\frac{S}{\sqrt{n} } }[/tex]
Where x is the sample mean
u is the population mean
s is the standard deviation
n is the sample size.
The hypothesis are: H0 : μ = 20 V/s H1 : μ > 20
We have x = 21.1
u = 20
s = 4.3
n = 35
Putting these values in the above formula, we get:
[tex]\rm Z= \frac{(21.1-20)}{\frac{4.3}{\sqrt{35} } }\\\\\rm Z= \frac{(1.1)}{\frac{4.3}{\sqrt{35} } }\\\\[/tex]
Z = 1.513
difference or df = n -1 ⇒ 35-1 ⇒ 34
P-value at (1.513, 34) = 0.06976 (From the p-value calculator)
P-value = 0.0698 (Rounded to 4-decimal places)
Thus, the p-value is 0.0698 if rounded to 4-decimal places.
Learn more about the standard deviation here:
brainly.com/question/12402189
Describe domain and range of the graph.
Complete the equation describing how X and Y are related X= -2, -1, 0, 1,2,3. Y= -8, -5,-2,1,4,7
Answer:
y = 3x - 2
Happy Studying
From the picture, two cylindrical glasses of the same capacity. Find the diameter length (X) of a small glass of water.
8
12
14
10
Answer:
12
Step-by-step explanation:
πr²h=πr²h
π(4.5)²*10=π(x/2)²4.9
15. On Sports Day, Mike runs 100 metres in 13.89 seconds and Neal runs the same distance in 13.01 seconds. Who is the FASTER runner?
Answer:
Neal
Step-by-step explanation:
13.01 < 13.89
Hey community I thank you guys fir your help
Answer:
A, B, and E.
Step-by-step explanation:
A. 5^x * 5^x
= 5^x+x
=5^(2)(x)
=25^x
B. 5^2x
=5^(2)(x)
=25^x
C. 5*5^2x
=5^1+2x
D. 5*5^x
=5^1+x
E. (5*5)^x
=5^x*5^x
=5^(2)(x)
=25^x
F. 5^2*5^x
=5^2+x
X ^2 + 2x + y’ + 6y = 15
Step-by-step explanation:
x^2+2x+7y=15
7y=15-x^2-2x
y=15/7-1/7x^2-2/7x , x ∈ all real numbers
if "-3<" x/5 < "-1" what is the value of x
Answer:
-15 < x < -5
Step-by-step explanation:
-3 < x/5 < -1
Multiply all sides by 5
-3*5 < x/5 *5 < -1*5
-15 < x < -5
Next question
lets keep going
Answer:
U = 67.6 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos U = adj side / hypotenuse
cos U = sqrt(10)/ sqrt(69)
cos U = sqrt(10/69)
Taking the inverse cos of each side
cos ^-1( cos U) = cos ^-1(sqrt(10/69))
U = 67.62335
To the nearest tenth
U = 67.6 degrees
Step-by-step explanation:
here's the answer to your question
Does the function ƒ(x) = (1∕2) + 25 represent exponential growth, decay, or neither?
A) Exponential growth
B) Impossible to determine with the information given.
C) Neither
D) Exponential decay
Answer:
A) Exponential growth
Step-by-step explanation:
I NEED HELP ON C,E,F,G PLEASE ASAP!!!!
Find the missing length in the image below
Answer:
not similar
Step-by-step explanation:
32/26 = 16/13
18/12 = 3/2
16/13 is not equal to 3/2, so the rectangles are not similar.
Lets check
[tex]\\ \sf\longmapsto \dfrac{32}{18}\boxed{}\dfrac{26}{12}[/tex]
[tex]\\ \sf\longmapsto \dfrac{16}{9}\boxed{}\dfrac{13}{6}[/tex]
Hence
[tex]\\ \sf\longmapsto \dfrac{16}{9}\neq\dfrac{13}{6}[/tex]
Both rectangles are not similar
how to work this fraction 4/11+5/22+3/44
Answer:
29/44
Step-by-step explanation:
[tex]\frac{4}{11} +\frac{5}{22} +\frac{3}{44} =\\[/tex]
-find the common denominator
[tex]\frac{4*4}{4*11} + \frac{2*5}{2*22} +\frac{3}{44} =[/tex]
[tex]\frac{16}{44} +\frac{10}{44} +\frac{3}{44} =[/tex]
-add the fractions and solve
[tex]\frac{16+10+3}{44} =[/tex]
[tex]\frac{29}{44}[/tex]
guys help me I really need your help
Answer:
a x^2/2 is a polynomial because the power of x is 2 which is a positive whole number but 2/x^2 is not a polynomial because the power of x is -2 which is negative whole number.
b.in
[tex] \sqrt{2 x} [/tex]
the power if x will be
[tex]x {}^{ \frac{1}{2} } [/tex]
which is not a whole number so it is not a polynomial.
but in
[tex] \sqrt{2} x[/tex]
the power if x is a positive whole number.so it is a polynomial.
c.the greatest power of variable of the term is called degree of polynomial
Select the statement that best justifies the conclusion based on the given information.
a. Definition of bisector.
b. Definition of midpoint.
c. If two lines intersect, then their intersection is exactly one point.
d. Through any two different points, exactly one line exists.
9514 1404 393
Answer:
a. Definition of bisector.
Step-by-step explanation:
Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.
The conclusion is justified by the definition of a bisector.
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) F(x) = sin(x/2) , [π/2,3π/2]
Answer:
The numbers 3(pi)/2, 5(pi)/2 satisfy the conclusion of Rolle's Theorem
Step-by-step explanation:
1. The function must be continuous.
Trigonometric functions are continuous.
2. It must be true that f(a) = f(b) = 0
For this case sin(pi) = sin(3pi) = 0
3. Therefore by Rolle's Theorem, there exist a point, x, such that f(x) = 0
For this case f(x) = cos(x)
And cos(x) = 0 at x = 3(pi)/2,5(pi)/2
