Answer:
32
P = 100 × 32%(0.32) = 32
Answer:
32
Step-by-step explanation: You multiply 100 by 0.32 which is 32% as a decimal
what is the volume of a cylinder, in cubic feet, with a height of 8 feet and a base diameter of 18 Round to the nearest place
Find the surface area and volume of the figure below. Round your answers to the nearest tenth. (50 pts)
Answer:
Surface Area = 188.4 square yardsVolume = 216 cubic yardsStep-by-step explanation:
Finding the hypotenuse of the triangular side :
Applying Pythagorean theorem√6² + 6²√2 x 6²6√2Finding Surface Area :
Area (2 triangles) + Area (2 smaller rectangles) + Area (larger rectangle)2 x 1/2 x 6 x 6 + 2 x 12 x 6 + 12 x 6√236 + 144 + 6√2180 + 6√26 (30 + √2)6 (30 + 1.4)6 (31.4)188.4 square yardsFinding Volume :
1/2LWH1/2 x 12 x 6 x 66³216 cubic yardsFind f¹(x) for the function f(x)= x/3
f¹(x) = [?]x
Answer:
3x
Step-by-step explanation:
f(x) = x/3
let , y=f(x)
or y=x/3
inter changing x and y, we get,
x=y/3
or, 3x=y. ( cross multiplication)
therefore f-1(x) 3x
Decide whether you have enough information to determine that the triangles are congruent. If they are congruent, explain why.
A. On place 20000 f à intérêt composé au taux annuel t%. Au
bout d'un an on complète par un dépôt de 20000 f. Un an
après ce nouveau placement on retire la totalité soit :
44298 f. Calculer le taux t.
Answer:
Step-by-step explanation: Après un an on a 20000(1+t%)+20000
Après 2 ans on a 20000(1+t%)^2+20000(1+t%)^1=44298
On a donc 20000[(1+t%)^2+(1+t%)^1]=44298
En résolvant l’équation de second degré dans R, on obtient : t = 7%
What is the height of the trapezoid?
Answer:
11 units
Step-by-step explanation:
The height of a trapezoid is the distance between the parallel bases.
__
Here, one base lies on the horizontal line y=5, and the other lies on the horizontal line y = -6. The distance between them is ...
5 -(-6) = 5 +6 = 11
You can also find this distance by counting the grid squares between the two parallel lines.
The height of the trapezoid is 11 units.
_____
Additional comment
The base lengths are ...
AB = 2 -(-5) = 7
CD = 8 -(-7) = 15
The area is 1/2(b1 +b2)h = (1/2)(7 +15)(11) = 121 square units.
Let A x B = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6)} then, find A, B, n(A), n(B).
Answer:
Step-by-step explanation:
A={1,2,3}
n(A)=3
B={5,6}
n(B)=2
4. Make a table and graph the function. (1 point)
y = 4x + 2
Write a sine function that has an amplitude of 5, a midline of 4 and a period of
4
Answer:
See below
Step-by-step explanation:
Start with sin x
amplitude of 5
5 sin x
midline 4
5 sin (x) + 4
period of 4
2 pi / 4 = pi/2
5 sin ( x pi/2 ) + 4
Can anyone please solve this for me right now?
The population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.
What is an exponential function?Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The population model, which describes the population of a country in millions t years after the 2003 is,
[tex]A=645.4 e^{0.001t}[/tex]
For the year 2003 the value of t will be 0 as no year is passed after 20036. Thus,
[tex]A=645.4 e^{0.001\times0}\\A=645.4 e^{0}\\A=645.4(1)\\A=645.4[/tex]
Thus, the population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.
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is 300 greater than 8/9?
Answer:
yes.
Step-by-step explanation:
300>8/9
300>0.888888889
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Is 300 greater than 8/9?
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Yes, 300 is greater than [tex]\bold{\dfrac{8}{9}}[/tex].
Remember, proper fractions (fractions with a numerator less than the denominator) are less than 1.
When comparing an integer (like 300) with a fraction (like 8/9), first you need to work out whether or not the fraction is a proper fraction.
Then, you also need to pay attention to the signs, because they may seem trivial, but they are in fact highly significant.
Therefore,
300>8/9 (300 is definitely greater than a number less than 1, right?)
(and the ">" sign means "greater than"
Good luck with your studies.[tex]\rule{200}{2}[/tex]
the perimeter of a rectangle is 26 and the area is 30. what are the dimensions of the rectangle ?
Answer:
Step-by-step explanation:
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
The linear inequality is represented by the graph will be, y > 3x + 2. Option B is correct.
What is linear inequality?Linear inequalities involve at least one linear algebraic expression. A polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1.
The line is passes through the following points;
(x₁,y₁) to (x₂,y₂)
(-3,-7) to (0,2)
The equation is found as;
[tex]\rm y-y_1 = \frac{y_2-y_1}{x_2-x_1 } (x-x_1)\\\\\ \rm y-(-7) = \frac{(2-(-7))}{(0-(-3))} (x-(-3))\\\\ y+7 =\frac{9}{3} (x+3)\\\\ y+7 = 3x+9 \\\\ y=3x+2[/tex]
The graph because the shading is above the line and does not include the line.
The linear inequality is represented by the graph will be, y > 3x + 2
Hence, option B is correct.
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Select the reason that best supports statement 5 in the given proof. (See Image)
A distributive property
B substitution
C reflective property
D subtraction property of equality
Answer:
Substitution
Step-by-step explanation:
In your premises, the state AB = BC is given to be true. In math, substitution is taking one value in an equation and "subbing it out for" one that we know has the same value. This means anywhere we see AB, we can substitute BC and the equation will still be true, because AB = BC.
In the example given, that changes AB + BC = AC to AB + AB = AC.
We substituted the AB with BC, because we know that they are of the same value.
Pedro is sailing his boat and maps his route on a coordinate plane. He starts at the origin and then sails 1.2 kilometers west, 1.5 kilometers south, 2 kilometers west again, and 2.8 kilometers north.
Pedro's total distance moved is 7.5 kilometers
How to determine the total distance?The given parameters are:
West = 1.2 kilometersSouth = 1.5 kilometers West = 2 kilometersNorth = 2.8 kilometersThe total distance is the sum of the above distances i.e.
Total = 1.2 km + 1.5 km + 2 km + 2.8 km
Evaluate
Total = 7.5 km
Hence, Pedro's total distance moved is 7.5 kilometers
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WILL MARK BRAINLIEST The amount (A) that principal (P) will be worth after t years at interest rate (r) compounded annually is
A = P(1 + r)
t
Suppose $6,000 is invested at 5.5% and yields a total of $7,255. How many years was it invested?
Put in the formula
[tex]\\ \rm\Rrightarrow A=P(1+r)^t[/tex]
[tex]\\ \rm\Rrightarrow 7255=6000(1+0.055)^t[/tex]
[tex]\\ \rm\Rrightarrow 1.20917=(1.055)^t[/tex]
[tex]\\ \rm\Rrightarrow ln1.20917=tln1.055[/tex]
[tex]\\ \rm\Rrightarrow t=\dfrac{ln1.20917}{ln1.055}[/tex]
[tex]\\ \rm\Rrightarrow t=3.5years[/tex]
Answer:
4 years (nearest year) or
3.5 years (nearest tenth) or
3 years, 6 months and 17 days (most accurate)
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
A = $7,255P = $6,000r = 5.5% = 0.055Substitute the given values into the formula and solve for t:
[tex]\implies \sf 7255=6000(1+0.055)^t[/tex]
[tex]\implies \sf 7255=6000(1.055)^t[/tex]
[tex]\implies \sf \dfrac{7255}{6000}=(1.055)^t[/tex]
Take natural logs of both sides:
[tex]\implies \sf \ln \left(\dfrac{7255}{6000}\right)= \ln (1.055)^t[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies \sf \ln \left(\dfrac{7255}{6000}\right)= t\ln (1.055)[/tex]
[tex]\implies \sf t=\dfrac{\ln \left(\dfrac{7255}{6000}\right)}{\ln (1.055)}[/tex]
[tex]\sf \implies t=3.547416819...[/tex]
Therefore, the number of years the principal was invested is:
4 years (nearest year)3.5 years (nearest tenth)3 years, 6 months and 17 daysLearn more about compound interest here:
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Can someone explain how to solve this I’m confused
Answer:
x = 61°
Step-by-step explanation:
(2x + 3)°+ (x - 6)° = 180°
2x + x + 3 - 6 = 180°
3x - 3 = 180°
3x = 180° + 3
3x = 183°
x = 183°/3
x = 61°
The sum of four consecutive even numbers is 60. Find the smallest of the four number.
Answer:
answer = 12
Step-by-step explanation:
Let the smallest number be x
So
X+(x+2)+(x+4)+(x+6)=60
4x+12=60
4x=48
X=12
Simplify, y-8(y+12) + 4
NEED HELP
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{y - 8(y + 12) + 4}[/tex]
[tex]\huge\textbf{Solving:}[/tex]
[tex]\mathbf{y - 8(y + 12) + 4}[/tex]
[tex]\huge\textbf{DISTRIBUTE -8 WITHIN the}\\\\\\\huge\textbf{PARENTHESES:}[/tex]
[tex]\mathbf{= y - 8(y) - 8(12) + 4}[/tex]
[tex]\mathbf{= y - 8y - 96 + 4}[/tex]
[tex]\huge\textbf{COMBINE the LIKE TERMS:}[/tex]
[tex]\mathbf{= (y - 8y) + (-96 + 4)}[/tex]
[tex]\mathbf{= y - 8y - 96 + 4}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{ = -7y - 92}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathbf{ -7y - 92}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Angelica places an 8-foot ladder against a wall. The ladder is placed so that the angle of elevation is 70°. How far up the wall, in feet, does the ladder reach? Round to the nearest hundredth.
The height of the ladder far up the wall to the nearest hundredth is 7.52 foot.
A right angle triangle is formed.
What is a right angle triangle?A right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.
The length of the ladder is the hypotenuse side of the triangle formed.
Therefore,
sin 70 = opposite / 8
cross multiply
opposite = 8 sin 70
opposite side = 8 × 0.93969262078
opposite side = 7.51754096629
opposite side = 7.52
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in a hostel of 400 students, it was discovered that 70% like to drink tea and 60% like to drink coffee . if 10% students didn't like to drink tea or coffee , represent the information in a venn-diagram and find the number of students who like 1)coffee only,tea, bothtea and coffee ,neither tea nor coffee
Of the 400 students, 120 students like to drink coffee, 80 students like to drink tea, 160 students like both and 40 students do not like any of these drinks.
How many students like to drink coffee, tea, or none?Cofee: 70% of 400 = 280 students
Tea: 60% of 400 = 240 students
None: 10% of 400= 40 students
This means that 360 students like coffee, tea or both.
How many students like both drinks?280 + 240 (students who drink either coffe or tea)= 520 - 360 (real number of students who like coffee or tea) = 160 (students who like both coffee and tea.
Moreover, it can be inferred 80 students like tea and 120 studetns like coffee.
How to represented it in a Venn diagram?Set A: Students who like coffee 120 students.Set B: Students who like tea 80 students.Set A^B: Students who ike both drinks 160 studentsOutside the sets 40 students who do not like any of the drinks.
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What is the approximate area of the shaded sector in the circle shown below?
100°
c
18 cm
O A. 31.4 cm2 O B. 565 cm O C. 15.7 cm O D. 283 cm2
Answer:
C
Step-by-step explanation:
Formula to get the area
A = r^2π
A = 16^2π
A= 804.24 cm^2
As per the given data, the approximate area of the shaded sector is 283 square cm, which is option D.
What is area?Area is a measure of the amount of space inside a two-dimensional shape or a flat surface. It is typically measured in square units, such as square meters or square feet.
To find the area of the shaded sector, we need to first find the area of the whole circle, and then multiply it by the fraction of the circle that is shaded.
The area of a circle is given by the formula:
A = [tex]\pi r^2[/tex]
Where r is the radius of the circle. In this case, we are given that the radius of the circle is 18 cm, so we can substitute this value into the formula:
A = [tex]\pi 18^2[/tex]
A = 324π
So, the area of the whole circle is 324π square cm.
The shaded sector has a central angle of 100 degrees, which is a fraction of the total central angle of 360 degrees. So, the fraction of the circle that is shaded is:
100° / 360° = 5/18
Therefore, the area of the shaded sector is:
A = (5/18) * 324π
A = 90π
Using 3.14 as an approximation for π, we get:
A ≈ 90 * 3.14
A ≈ 283
Thus, the approximate area of the shaded sector is 283 square cm, which is option D.
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Simplify 5(xy+z)-2xy.
Answer:
3xy+5z
Step-by-step explanation:
5(xy+z)-2xy
=5xy+5z-2xy
3xy+5z
Find the missing values. Leave answers in simplified radical form.
Answer:
See below ~
Step-by-step explanation:
Q3
r = 8 / sin 45°r = 8 / (1/√2)r = 8√2t = 8 / tan 45°t = 8 / 1t = 8
Q4
f = 9√3 / sin 60°f = 9√3 / (√3/2)f = 18o = 9√3 / tan 60°o = 9√3 / √3o = 9#3
tan45=8/t1=8/tt=8Simiilary
cos45=8/rr=8√2#4
sin60=9√3/f√3/2=9√3/f1/2=9/ff=18And
cos60=0/181/2=0/18o=18/2=9what is "the power" of something (mathematically).
The power of a number says how many times to use the number in a multiplication.
--
For instance 6 to the power of 2
This means
6²Which is also equal to 36
What is the length of the hypotenuse?
Answer:
Step-by-step explanation:
First things first, let's explain what a right triangle is. The definition is very simple and might even seem obvious for those who already know it: a right-angled triangle is a triangle where one and only one of the angles is exactly 90°. The other two angles will clearly be smaller than the right angle because the sum of all angles in a triangle is always 180°. In a right angled triangle the sides are defined in a special way. The side opposing the right angle is always the biggest in the triangle and receives the name of "hypotenuse". The other two sides are called catheti. The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c².
To solve for c, take the square root of both sides to get c = √(b²+a²). This extension of the Pythagorean theorem can be considered as a "hypotenuse formula".
Steps to solve:
[tex]c=\sqrt{a^{2} +b^{2} } \\c=\sqrt{1.3^{2} +6.1^{2} } \\c=\sqrt{1.69+37.21} \\c=\sqrt{38.9} \\c=6.236986[/tex]
(05.07) A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
19.25 cm2
30.625 cm2
49.625 cm2
61.25 cm2
The surface area of the square based pyramid is 61.25 centimetre square
How to find the surface area of a square base pyramid?surface area of the pyramid = A + 1 /2 ps
where
A = area of the base
p = perimeter of the base
s = slant height
Therefore,
A = 3.5² = 12.25 cm²
p = 4(3.5) = 14 cm
s = 7 cm
Therefore,
surface area of the pyramid = 12.25 + 1 /2 × 14 × 7
surface area of the pyramid = 61.25 cm²
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which is a solution to x - 3x + 9 equals negative 27
Answer:
x = 18
Step-by-step explanation:
[tex]\sf x - 3x+9= - 27[/tex]
Let's first combine like terms.
[tex] \sf - 2x+9= - 27[/tex]
Subtract 9 from both sides.
[tex]\sf - 2x= - 27 - 9[/tex]
[tex] \sf - 2x= - 36[/tex]
Divide both sides by −2.
[tex]\sf x=18[/tex]
5.
In the parallelogram ABCD, the diagonals AC and BD
are equal in length. What is the measure of the angle A
?
two
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
How to solve this?
Answer:
(E) 90°
Step-by-step explanation:
The diagonals of a parallelogram are equal in length if and only if the parallelogram is a rectangle.
Any angle of a rectangle is 90°.
_____
Adjacent angles of a parallelogram are supplementary. If the diagonals are the same length, the triangles formed by either diagonal are congruent with the triangles formed by the other diagonal. This means adjacent angles are congruent. Congruent supplementary angles are 90°.
In November 2005, an international study to assess public opinion on the treatment of suspected terrorists was conducted (“Most in U.S., Britain, S. Korea, and France Say Torture is OK in at Least Rare Instances,” Associated Press, December 7, 2005). Each individual in random samples of 1000 adults from each of 9 different countries was asked the following question: “Do you feel the use of torture against suspected terrorists to obtain information about terrorism activities is justified?” Responses from Italy, Spain, France, the United States, and South Korea are summarized in the table below. Based on these data, is it reasonable to conclude that the response proportions are not the same for all five countries? Use a = 0.01 to test the appropriate hypotheses.
Based on the responses, the significance level, and the p-value, we can conclude that the response proportions are not the same for the countries.
What can be concluded about the response proportions for these countries?The null hypothesis is that the response proportions are the same. The alternate hypothesis is that the response proportions are not the same.
The sample size is large enough for a Chi-Square test to be used because the expected counts are all greater than 5.
Running a Chi-Square analysis shows that the P-value to be 0.000.
The P-Value is less than the significance level of 0.01 so the null hypothesis is rejected. This means that the alternate hypothesis of the response proportions not being the same is true.
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