Answer:
piece of wire 8 m long
one piece is bent into square:
the square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side=1 m.
the perimeter of the square =2L+2W=2(1)+2(1)=4 m
that is the max. amount can be cut from the wire, since the other part is bent into a circle.
( note if you cut more, the square will take the whole wire)
Perimeter=2L+2W=2(2)=2(2)=8 m and the area=2*2=4 m²)
Area and perimeter are two crucial characteristics of 2D shapes in mathematics.
The perimeter of the square exists 8 m and the area exists 4 m².
What is the perimeter and area of a square?Area and perimeter are two crucial characteristics of 2D shapes in mathematics. The area and perimeter both specify the shape's boundaries and the space they occupy, respectively. Area and perimeter are significant mathematical concepts that are used to daily life. All sizes and shapes, regular or unusual, are covered by this. Each shape's area and perimeter calculations are unique.
Piece of wire is 8 m long and one piece is bent into square:
The square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side = 1 m.
The perimeter of the square = 2L + 2W = 2(1) + 2(1) = 4 m
Which exists the maximum amount that can be cut from the wire, since the other part is bent into a circle.
Perimeter = 2L + 2W =2(2) = 2(2) = 8 m and the area = 2 × 2= 4 m²
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A cell phone company offers a plan that costs $35 per month plus an additional cost of $0.08 per text message.
Write an equation to represent this problem.
Answer:
C = 35 + 0.08t
Step-by-step explanation:
The equation is:
35 + 0.08t = C
C = Cost by month
t = cost for each additional message
Please help me with this answer!! I am really stuck...No nonsense answers please.
Answer:
19
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
< DBG = 1/2 ( DG)
< DBG = 1/2 ( 360 - BD - BG)
= 1/2 ( 360 - 172 - 150)
= 1/2 (38)
= 19
Petroleum motor oil does a combination of natural oil and synthetic oil. It contains 5 L of natural oil for every 3 L of synthetic oil. In order to make 768 L of petroleum oil how many liters of natural oil are needed
Answer:
480 liters of natural oil
Step by step Explanation:
ratio of natural to synthetic oil
= 5:3
If 440 liters have to be made then,
Add 5 + 3 = 8
So, 5/8 of 768 liters will be = 480 liters of natural oil
and, 3/8 of 768 liters will be = 288liters of synthetic oil
Therefore, 480 liters of natural oil will be needed
Susan purchased 9/10 of a pound of shrimp for a dinner party. Her plan is to serve 1/6 of a pound of shrimp to herself and each guest. Including herself, how many people can Susan serve at her dinner party? (Remember that you can't have a fraction of a person.)
Answer:
Susan and 4 quests
5 people
Step-by-step explanation:
Take 9/10 and divide by 1/6
9/10 ÷1/6
Copy dot flip
9/10 * 6/1
54/10
50/10 + 4/10
5 4/10
We can only serve whole numbers
5 people
Susan and 4 quests
Find the probability of rolling a three first and then a ten when a pair of dice is rolled twice
Answer: 0.0046
Step-by-step explanation:
First, let's calculate the total number of outcomes that you can see from a pair of dice.
Each dice has 6 options, so the total number of combinations is:
6*6 = 36.
Now, the combinations that are equal to 3 are:
3 and 1
1 and 3
2 combinations.
So the probability is equal to the quotient between the number of combinations that are equal to 3, and the total number of combinations:
P = 2/36 = 0.055
Now, the combinations that are equal to 10 are:
5 and 5
4 and 6
6 and 4.
3 combinations.
Then the probability is:
P = 3/36 = 0.0833
Now, the probability of both events happening is equal to the product of the probabilities for each event, so the total probability is equal to:
P = ( 0.0833)*( 0.055) = 0.0046
What is the slope of line m?
Answer:
2.
Step-by-step explanation:
The slope is calculated by doing rise over run.
The rise is: 6 - 0 = 6.
The run is: 0 - (-3) = 0 + 3 = 3.
6 / 3 = 2 / 1 = 2.
Hope this helps!
Which are correct representations of the inequalities 6x>3+4(2x-1)?
select three options.
1st 2nd and last
Step-by-step explanation:
simplify your inequality
6x >= 3 + 4(2x -1)
6x >= 3 + 8x - 4
2x >= 1
x >= 1/2
so indeed the
1st one , the 2nd and the last one
first, second, last
Hope it helps
James determined that these two expressions were equivalent expressions using the values of y=4 and yu 6. Which
statements are true? Check all that apply
7x+4 and 3x+5+4x-1
When - 2. both expressions have a value of 18.
The expressions are only equivalent for X-4 and X- 6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When - 0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if X-
Answer with explanation:
Two or more Algebraic expressions are said to be equivalent, if both the expression produces same numerical value , when variable in the expressions are replaced by any Real number.
The two expressions are
1. 7 x +4
2. 3 x +5 +4 x =1
Adding and subtracting Variables and constants
→7 x +5=1
→7 x +5-1
→7 x +4
→ When x=2,
7 x + 4 =7×2+4
=14 +4
=18
So, Both the expression has same value =18.
→So, by the definition of equivalent expression, when ,you substitute , x by any real number the two expression are equivalent.
Correct options among the given statement about the expressions are:
1.When x = 2, both expressions have a value of 18.
2.The expressions have equivalent values for any value of x.
3.The expressions have equivalent values if x = 8.
Find the value of x.
Answer:
8.8Option A is the correct option.
Step-by-step explanation:
As PW is the median.
PW = [tex] \frac{1}{2} [/tex] ( YZ + TM )
Plug the values
x = [tex] = \frac{1}{2} (5.5 + 12.1)[/tex]
Calculate the sum
x = [tex] = \frac{1}{2} \times 17.6[/tex]
Calculate the product
x = [tex] = 8.8[/tex]
Hope this helps...
Best regards!
Determine the value of x.
Answer:
B. 6sqrt(2).
Step-by-step explanation:
Since the two legs of the right triangle are congruent, this is a 45-45-90 triangle. That means that the hypotenuse will measure xsqrt(2) units, and each leg will measure x units.
In this case, x = 6.
So, the hypotenuse is B. 6sqrt(2).
Hope this helps!
a car is driving at a speed of 40mi/h.what is the speed of the car in feet per minute
Answer:
[tex]\boxed{3520\ ft/min}[/tex]
Step-by-step explanation:
1 miles per hour = 88 feet per minute
Multiplying both sides by 40
40 miles per hour = 88*40 ft/min
40 mi./hr = 3520 ft/min
Answer:
3520 feet/min
Step-by-step explanation:
the speed of the car in feet per minute:
first convert miles to feet ( 1 mile =5280 feet) and hours to minutes(1hr=60min.)
(40*5280)/1*60=3520 feet/min
simplify (5 √2 - 1) ^2
If log3=0.4771 and log2=0.3010,Find the value of log12
Answer:
log 12 = 1.0761
Step-by-step explanation:
log 12
=log(3*2*2)
= log 3 +log 2+ log 2
=0.4771+0.3010+0.3010
=1.0761
Answer:
Log 12 = 1.0791
Step-by-step explanation:
=> log (12)
Prime Factorizing 12
=> log (2×2×3)
Using log rule : [tex]log (a*b) = log a+logb[/tex]
=> Log 2 + log 2 + log 3
Given that log 2 = 0.3010 , log 3 = 0.4771
=> 0.3010 + 0.3010 + 0.4771
=> 1.0791
Please help I don't understand
Answer:
£531.52
Step-by-step explanation:
We are given the profit in week 1 and information about week 2. We are asked for the difference between week 2 profit and week 1 profit.
__
In week 2, pizza is sold 4 ways. The diagram shows the numbers of pizzas sold each way. The table shows the profit made for each way the pizza was sold. We need to add up the profits from each of the sales to find the profit for week 2.
10-inch/normal price: profit = 407×£3.72 = £1514.0410-inch/offer price: profit = 358×(-£0.49) = -£175.4212-inch/normal price: profit = 169×£5.26 = £888.9412-inch/offer price: profit = 142×(-£0.04) = -£5.68Then the total profit in week 2 is ...
£1514.04 -175.42 +888.94 -5.68 = £2221.88
So, profit in week 2 exceeds profit in week 1 by ...
£2221.88 -1690.36 = £531.52 . . . more profit in week 2
Please give me the correct answer her please
Answer:
9.3 inStep-by-step explanation:
m∠UTV = 112° ⇒ m∠WTV = 180° - 112° = 68°
sin(68°) ≈ 0.9272
sin(∠WTV) = WV/TV
WV/10 ≈ 0.9272
WV ≈ 9.272
WV ≈ 9.3
The slope of the line below is 4 . Which of the following is the point slope form of that line ? ( top answer gets )
Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 4 and (a, b) = (- 3, - 4) , thus
y - (- 4) = 4(x - (- 3)) , that is
y + 4 = 4(x + 3) → C
If I mix 5 gallons of p% boric acid with 5 gallons of water, what is the concentration of the mixture?
Answer: The concentration of the mixture is 0.5 p % .
Step-by-step explanation:
Given: 5 gallons of p% boric acid is mixed with 5 gallons of water.
Amount of boric acid = p% of 5 gallons
[tex]=\dfrac{p}{100}\times5\text{ gallons}= 0.05p\text{ gallons}[/tex]
Total solution : 5 +5 = 10 gallons
then, the concentration of the mixture = [tex]\dfrac{\text{Amount of boric acid in solution}}{\text{Total solution}}\times100[/tex]
[tex]=\dfrac{0.05p}{10}\times100\\\\=0.5p[/tex]
Hence, the concentration of the mixture is 0.5 p % .
Answer:
0.5p% is the answer
FInd the Slope and y-intercept
3y-x=18
Answer:
The slope is 1/3 and the y intercept is 6
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
3y -x =18
Add x to each side
3y = x+18
Divide each side by 3
3y/3 = x/3 +18/3
y = 1/3x +6
The slope is 1/3 and the y intercept is 6
We need to solve for y (y = mx + b):
3y - x = 18
~Add x to both sides
3y = 18 + x
~Divide 3 to everything
y = 6 + x/3 or y = 6 + 1/3/x
So... 1/3 is the slope and 6 is the y-intercept.
Best of Luck!
Find the inverse of the function f(x) = 2x² - 3x NO ABSURD ANSWERS IF YOU DON't WANT YOURSELVES TO GET REPORTED!
Answer:
[tex]\boxed{f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}}[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2-3x[/tex]
[tex]f(x)=y[/tex]
[tex]y=2x^2-3x[/tex]
Switch variables.
[tex]x=2y^2-3y[/tex]
Solve for y.
Multiply both sides by 8.
[tex]8x=16y^2-24y[/tex]
Add 9 on both sides.
[tex]8x+9=16y^2-24y+9[/tex]
Take the square root on both sides.
[tex]\sqrt{8x+9} =\sqrt{16y^2-24y+9}[/tex]
Add 3 on both sides.
[tex]\sqrt{8x+9}+3 =\sqrt{16y^2-24y+9}+3[/tex]
Divide both sides by 4.
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{\sqrt{16y^2-24y+9}+3}{4}[/tex]
Simplify.
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y-3+3}{4}[/tex]
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y}{4}[/tex]
[tex]\frac{\sqrt{8x+9}+3}{4}=y[/tex]
Inverse y = [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}[/tex]
Answer:
[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
Step-by-step explanation:
[tex] f^{-1}(x) = 2x^2 - 3x [/tex]
Change function notation to y.
[tex] y = 2x^2 - 3x [/tex]
Switch x and y.
[tex] x = 2y^2 - 3y [/tex]
Solve for y.
[tex] 2y^2 - 3y = x [/tex]
Complete the square on the left side. We must divide both sides by 2 to have y^2 as the leading term on the left side.
[tex] y^2 - \dfrac{3}{2}y = \dfrac{x}{2} [/tex]
1/2 of 3/2 is 3/4. Square 3/4 to get 9/16.
Add 9/16 to both sides to complete the square.
[tex] y^2 - \dfrac{3}{2}y + \dfrac{9}{16} = \dfrac{x}{2} + \dfrac{9}{16} [/tex]
Find common denominator on right side.
[tex] (y - \dfrac{3}{4})^2 = \dfrac{8x}{16} + \dfrac{9}{16} [/tex]
If X^2 = k, then [tex] X = \pm \sqrt{k} [/tex]
[tex] y - \dfrac{3}{4} = \pm \sqrt{\dfrac{1}{16}(8x + 9)} [/tex]
Simplify.
[tex] y = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
Back to function notation.
[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
-3 raised to 2 + -3 raised to 2 =
Answer:
Step-by-step explanation:
(-3)² + (-3)² = (-3)*(-3) + (-3)*(-3)
= 9 + 9
= 18
Answer:
18
Step-by-step explanation:
Help somebody please!!Thank you
The diagonal of the square is the same as the diameter of the circle.
So, the diameter of the circle is 36.
Circumference formula:
C = 2πr
To find the radius, we just need to divide the diameter by two:
36 / 2 = 18
Now, solve using the given values.
C = 2π(18)
C = 36π
Therefore, the answer is D.
Best of Luck!
this is 69 points if you answer please help
Answer:
see below
Step-by-step explanation:
Angle C is equal to the 1/2 the difference of the two arcs
C = 1/2 ( large DC - small DC)
Large DC = ( 360 - 5x - 2) sum of a circle is 360 degrees
Small DC = 5x-2 the central angle is equal to the intercepted arc
C = 1/2 ( 360 - 5x-2 - ( 5x -2)) Angle Formed by Two Intersecting Chords
C = 1/2 ( 360 - 2 ( 5x-2))
Distributing the 1/2
C = 180 - (5x-2)
Replacing the C with 2x+7
2x+7 = 180 - (5x-2)
Add 5x-2 to each side
2x+7 +5x-2 = 180
Antonio is correct
Combine like terms
7x +5 = 180
7x = 175
Divide by 7
x =25
Then solve for A = 5x-2
A = 5*25-2
= 125-2
= 123
Be nice and answer my question
Answer:
look below
Step-by-step explanation:
hi
Use the interactive number line to find the sum.
-5.5 + 3.7 =
Answer: -1.8
Step-by-step explanation:
Start at -5.5 and move the point on the number line up 3.7 spaces.
Hope it helps <3
Answer:
Your correct answer is -1.8
Step-by-step explanation:
−5.5 + 3.7
= −5.5+3.7
= −1.8
Suppose instead of comparing independent measurements taken from two groups, you used a matched-pairs experiment and one treatment is randomly assigned to each half of the pair. In this case, how should you compute the confidence interval for the difference?
You should use a T distribution to find the critical T value based on the level of confidence. The confidence level is often given to you directly. If not, then look for the significance level alpha and compute C = 1-alpha to get the confidence level. For instance, alpha = 0.05 means C = 1-0.05 = 0.95 = 95% confidence
Use either a table or a calculator to find the critical T value. When you find the critical value, assign it to the variable t.
Next, you'll compute the differences of each pair of values. Form a new column to keep everything organized. Sum everything in this new column to get the sum of the differences, which then you'll divide that by the sample size n to get the mean of the differences. Call this dbar (combination of d and xbar)
After that, you'll need the standard deviation of the differences. I recommend using a calculator to quickly find this. A spreadsheet program is also handy as well. Let sd be the standard deviation of the differences
The confidence interval is in the form (L, U)
L = lower bound
L = dbar - t*sd/sqrt(n)
U = upper bound
U = dbar + t*sd/sqrt(n)
On a ski lift, the distance between chairs is inversely proportional to the number of chairs. At a
ski resort, one lift has 80 chairs spaced 16 meters apart. What is the constant of variation.
A.1280 B.5 C.1/5 D.1/1280
Constant of variation = number of chairs/ spacing.
80/16 = 5
The answer is B.5
¿que son los cuadriláteros?
Answer:
Cuadrilátero solo significa "cuatro lados" (quad significa cuatro, lateral significa lado). Un cuadrilátero tiene cuatro lados, es bidimensional (una forma plana), cerrado (las líneas se unen) y tiene lados rectos.
Un cuadrilátero es un polígono con cuatro aristas y cuatro vértices.
Step-by-step explanation:
Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000). An exit poll of 200 voters finds that 94 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52? Based on your result, comment on the dangers of using exit polling to call elections.
Answer:
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.
Step-by-step explanation:
From the information given :
An exit poll of 200 voters finds that 94 voted for the referendum.
How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52? Based on your result, comment on the dangers of using exit polling to call elections.
This implies that ;
the Sample size n = 200
the probability p = 0.52
Let X be the random variable
So; the Binomial expression can be represented as:
X [tex]\sim[/tex] Binomial ( n = 200, p = 0.52)
Mean [tex]\mu[/tex] = np
Mean [tex]\mu[/tex] = 200 × 0.52
Mean [tex]\mu[/tex] = 104
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{np(1-p)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(1-0.52)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(0.48)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{49.92}[/tex]
The standard deviation [tex]\sigma[/tex] = 7.065
However;
P(X ≤ 94) because the discrete distribution by the continuous normal distribution values lies in the region of 93.5 and 94.5 .
The less than or equal to sign therefore relates to the continuous normal distribution of X < 94.5
Now;
x = 94.5
Therefore;
[tex]z = \dfrac{x- \mu}{\sigma}[/tex]
[tex]z = \dfrac{94.5 - 104}{7.065}[/tex]
[tex]z = \dfrac{-9.5}{7.065}[/tex]
z = −1.345
P(X< 94.5) = P(Z < - 1.345)
From the z- table
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.
Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and leading coefficient. If the function is not a polynomial, state why. f(x)=x^4(2-x^3)+1
Answer:
The correct option is
This is a polynomial function of degree 7 with a leading coefficient of -1
Step-by-step explanation:
Functions that consist of a variable such as x raised to positive integer powers which are equal to or larger than zero added together to make the function are known as polynomial functions
Therefore, the function in the question which is f(X) = x⁴ × (2 - x³) + 1
Which can be expanded as follows
f(x) = 2·x⁴ - x⁷ + 1, which is the same as given as follow equation;
f(x) = -x⁷ + 2·x⁴ + 1
Which is polynomial function with a leading coefficient of -1 as it consists of only whole number positive powers of x including the powers of x 4 and 7
Therefore, the correct option is that f(x) is a polynomial function of degree 7 with a leading coefficient of -1.
PLZ HELP QUICK!!! - Fill in the missing values in the tables. If necessary, round your answer to three decimal places.
Answer:
first blank = 10 (for table 1)
second blank = 30 (for table 2)
====================================================
Explanation:
You could use a calculator to determine the value of b, then compute b^x for that first box. But as the instructions state, we don't need to use one. Why is that? Because the tables provide enough information to fill in the blanks.
Table 1 shows x = 2.096 lead to some unknown y value. Meanwhile, table 2 has x = 10 lead to y = 2.096; note the 2.096 shows up again. The exponential and log functions are inverses of each other. They undo each other's operation. This is similar to how division undoes multiplication, and vice versa.
Going in reverse of table 2, we will conclude that 10 must go in the blank for table 1. Therefore, b^x = 10 when x = 2.096
------------
Similarly, we will have 30 in the blank for table 2. Table 1 shows x = 3.096 lead to y = 30. Table 2 is the reverse of that as it is the inverse.
Throughout either section, we didn't need to find the value of b.
The missing value in table 1 is 10 and for table 2 it is 30.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
In the first table first column
x = 0.369 and bˣ = 1.5 ⇒
By logarithm
logbˣ = log1.5
xlogb = log1.5
Now x = 0.369
logb = 0.1760/0.369
b = 3
Now,
f(x) at x = 2.096 ⇒ [tex]3^{2.096}[/tex] = 10
And
x at g(x) = 3.096
[tex]log_{3}[/tex]x = 3.096 ⇒ x = 30.
Hence "The missing value in table 1 is 10 and for table 2 it is 30".
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