EXPLANATION
The module of any number, as in this case |a|, is the same number with positive sign, in this case the appropiate option is sqrt(a^2) ---> OPTION B.
What is the volume of this sphere?Use3.14 and round your answer to the nearest hundredth.4 mcubic metersHELPP!!!
Answer:
Explanation:
The formula for the area of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]Where r is the radius of the circle.
In this case, the diameter of the circle is 6in, then;
[tex]r=\frac{6in}{2}=3in[/tex]The volume is:
[tex]undefined[/tex]Solve the equation: √ t − 13 = 4 Answer: t =
Taking the given equation to the power of 2 we get:
[tex](\sqrt{t-13})^2=4^2.[/tex]Simplifying the above result we get:
[tex]t-13=16.[/tex]Adding 13 to the above equation we get:
[tex]\begin{gathered} t-13+13=16+13, \\ t=29. \end{gathered}[/tex]Answer: t=29.
write the sum in unit form. 4 fifths + 3 fifths =
We write it as follows:
[tex]\frac{4}{5}+\frac{3}{5}=\frac{7}{5}=1\frac{2}{5}[/tex]It is 1 unit and 2/5.
The table gives the temperature( in Fahrenheit) in five cities at 6 am on the same day please zoom in pic so its not blurry
(a)
Temp. in fairbanks is -29 if the temp. risen by 17 then temp. is:
[tex]\begin{gathered} \text{Present temp. =initial temp. }+\text{ change in temp.} \\ =-29+17 \\ =-12 \end{gathered}[/tex]In Noon the temp in fairbanks is -12 degree fehrebheit.
(b)
6 A.M temp in Santa =74
6 A.M. temp in toronto =-19
[tex]\begin{gathered} \text{change in temp.= high temp. - low temp.} \\ =74-(-19) \\ =74+19 \\ =93 \end{gathered}[/tex]In 6 A.M. temp 93 fehre
Need help with the question I need to understand so I do good on my test
Given:-
There are two types of log to measure the density.
Pine log of radius 5-inch and 30-inch long.
Oak board that is 5.5 inch long and 1.5 inch thickness and 3 feet long.
To find the shapes which can be used.
The pine long is round in shape so the shape formed in pine log is CYLINDRICAL SHAPE.
Oak board is 5.5 inch long and 1.5 inch thickness and 3 feet long so the shape formed will be CUBOID.
So the required solutions are CYLINDER AND CUBOID.
A training field is formed by Joining a rectangle and two semicircles, as shown below. The rectangle is 96 m long and 74 m wide.Find the area of the training fleld. Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
To calculate the area of the training field, the first step is to calculate the area of the rectangular portion. The formula for calculating the area of a rectangle is expressed as
Area = length x width
From the information given,
length = 96
width = 74
Area of rectangular portion = 96 x 74 = 7104
The two semicircles would add up to form a complete circle because a semicircle is half of a circle. The diameter of the circle would be the width of the rectangular portion. The formula for calculating the area of a circle is expressed as
Area = pi x radius^2
From the information given,
pi = 3.14
diameter = 74
radius = diameter/2 = 74/2 = 37
By substituting the values into the formula, we have
Area of the two semicircular portions = 3.14 x 37^2 = 4298.66
Area of the training field = area of rectangular portion + area of the two semicircular portions = 7104 + 4298.66
Area of the training field = 11402.66 m^2
Jimmy's school is selling tickets to a play. On the first day of ticket sales the school sold 12 senior citizentickets and 5 child tickets for a total of $173. The school took in $74 on the second day by selling 1 seniorcitizen ticket and 5 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
SOLUTION
Let s represent senior citizen tickets
and let c represent child ticket
On the first day the school sold 12 senior tickets and 5 child's tickets for $173.
This will be represented algebraically by 12s + 5c = 173 ..... equation 1
The following day they sold 1 senior ticket and 5 child's tickets for $74.
This will be represented by s + 5c = 74 ....... equation 2
Now we will solve equations 1 and 2 simultaneously we have
[tex]undefined[/tex]Find the slope of the line that passes through the points (15,-2) and (5,-4).Write answer as an integer or a reduced fraction
1) To find the slope of the line that passes through those points, we'll need to use the Slope Formula
[tex]\begin{gathered} m=\frac{y_2-y_1_{}}{x_2-x_1} \\ m=\frac{-4-(-2)}{5-15}=\frac{-4+2}{-10}=\frac{-2}{-10}=\frac{-1}{-5}=\frac{1}{5} \end{gathered}[/tex]Note that the slope is the measure of how steep is the line between those points.
2) That is the answer.
Phil wants to play full-back for his football team. The decision depends on who serves as head coach for a given game. Coach Sal is head coach about 75% of the time, and Coach Benny is head coach other 25% of the time. Coach Sal has faith in Phil, so he starts him at full-back in 70% of the games he coaches. Coach Benny is not so sure, so he starts Phil at full-back 30% of the time. What is the probability of Phil starting as full-back for the next game?0.3980.60.40.24
Given that
Coach Sal is the head coach about 75% of the time and coach Benny is the coach for the remaining 25% of the time.
Sal has faith in Phil, so he full-back in 70% of the time and Benny had the faith, so he full-back 30% of the time.
Explanation -
Since the coach, Sal is the coach for 75% of the time and Benny is for 25% of the time.
Also, Sal's faith in full-back is 70% and Benny's faith in full-back is 30%.
Then,
75% of 70% = 75/100 x 70/100 = 0.525
25% of 30% = 25/100 x 30/100 = 0.075
So the final probability of Phil will be 0.525 + 0.075 = 0.6
Final answer -
So the final answer is 0.6.Hence option B is correct.A triangle with side lengths 8, 15, and 17 is a right triangle by theconverse of thePythagorean Theorem. What are the measures of the other 2 angles?Round your answers to the nearest whole number.HINT: Draw a diagram of this problem and label your triangle.The méasure of the smaller acute angle is ____degreesand the larger acute angle measures_______degrees.
We are given a right-angle triangle with side lengths 8, 15, and 17.
Since it is a right triangle, one angle must be 90°
Let us find the other two angles of this right triangle.
With respect to angle x, the opposite side is 15 and the hypotenuse side is 17.
Recall from the trigonometric ratios,
[tex]\begin{gathered} \sin (x)=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin (x)=\frac{15}{17} \\ x=\sin ^{-1}(\frac{15}{17}) \\ x=61.9\degree \end{gathered}[/tex]So, the second angle is 61.9°
Recall that the sum of angles inside a triangle must be equal to 180°
So, the third angle can be found as
[tex]\begin{gathered} y+61.9\degree+90\degree=180\degree \\ y=180\degree-90\degree-61.9\degree \\ y=28.1\degree \end{gathered}[/tex]So, the third angle is 28.1°
The measure of the smaller acute angle is 28.1 degrees and the larger acute angle measures 61.9 degrees.
In AFGH, the measure of ZH=90°, GF = 89, HG = 80, and FH = 39. What ratiorepresents the cotangent of ZF?
cotangent ZF = adjacent side / opposite side
adjacent side = 39
opposite side = 80
cotangent ZF = 39/80
The length of a rectangle is given by the function l(x)=12x2+2x+4. The width of the rectangle is given by the function w(x)=3x−1.Which function represents the area of the rectangle?
The area of a rectangle is given by the next equation:
Area = Length * Width
Where
Length =1/2x²+2x+4.
and
Width = 3x−1
Replacing:
Area = (1/2x²+2x+4)* (3x-1)
Solve the operation:
(1/2x²* 3x) + (1/2x²*-1)+(2x*3x)+(2x*-1)+(4*3x)+(4*-1)
Simplify:
3/2x³-1/2x²+6x²-2x+12x-4
= 3/2x³+11/2x²+10x-4
Hence, the correct answer is a(x)=3/2x³+11/2x²+10x-4
Answer:a(x)=3/2x³+11/2x²+10x-4
Step-by-step explanation:
the volume of a recrangular prism is 72 centimeters.the prism is 2 centimeters wide and 4 centimeters high. what is the length of the prism
The volume of a rectangular prism is given by:
[tex]V=w\cdot l\cdot h[/tex]We know that the volume is 72 cub cm, the width is 2 cm and the height is 4 cm. Plugging this value in the equation we have:
[tex]72=2\cdot l\cdot4[/tex]Solving the equation for l we have:
[tex]\begin{gathered} 72=2\cdot l\cdot4 \\ 72=8l \\ l=\frac{72}{8} \\ l=9 \end{gathered}[/tex]Therefore the lenght of the prism is 9 cm.
Can someone help me with this geometry question I don’t know if I am right.
Let us find out if the given two triangles ABC and DEF are similar triangles or not.
Triangle ABC is a right-angled triangle so we can apply the Pythagorean theorem to find the missing side.
[tex]a^2+b^2=c^2[/tex]Where a and b are the shorter sides and c is the longest side (hypotenuse)
[tex]\begin{gathered} 20^2+21^2=c^2 \\ 400+441=c^2 \\ 841=c^2 \\ \sqrt[]{841}=c \\ 29=c \\ c=29 \end{gathered}[/tex]Similarly, we can apply the Pythagorean theorem to triangle DEF to find the missing side.
[tex]\begin{gathered} d^2+e^2=f^2 \\ 40^2+e^2=58^2 \\ e^2=58^2-40^2 \\ e^2=3364-1600 \\ e^2=1764 \\ e=\sqrt[]{1764} \\ e=42 \end{gathered}[/tex]Now, recall that two triangles are similar if the ratio of the corresponding sides is equal.
The corresponding sides are
AB = DE
BC = EF
AC = DF
[tex]\begin{gathered} \frac{DE}{AB}=\frac{EF}{BC}=\frac{DF}{AC} \\ \frac{40}{20}=\frac{42}{21}=\frac{58}{29} \\ \frac{2}{1}=\frac{2}{1}=\frac{2}{1} \end{gathered}[/tex]As you can see, the ratio of the corresponding sides of the two triangles is equal.
Hence, the triangles ABC and DEF are similar.
Frank has a vintage comic book worth $454. According to a dealer, the value of this particular comic book will increase by 15% each year. How much will the comic book be worth in 2 years?If necessary, round your answer to the nearest cent.
Given:
Current worth = $454
Rate of increase = 15% = 0.15
Time = t
To find how much the book will be worth in 2 years, apply the exponential growth formula:
[tex]y=a(1+r)^t[/tex]Where:
a is the current worth = 454
r is the rate of increase = 0.15
t is the time = 2 years
Hence, we have:
[tex]\begin{gathered} y=454(1+0.15)^2 \\ \\ y=454(1.15)^2 \\ \\ y=454(1.3225) \\ \\ y=600.42 \end{gathered}[/tex]Therefore, the worth of the comic book in 2 years is $600.42
ANSWER:
$600.422 ye
Solve in R Sin (x/4) = √2/2
Trigonometric Equations
Solve for x in R:
[tex]sin\text{ }\frac{x}{4}=\frac{\sqrt{2}}{2}[/tex]There are two angles whose sine is the given value: 45° and 135°. We need to express them in radians:
[tex]45^o=45\text{ }\frac{\pi}{180}=\frac{\pi}{4}[/tex][tex]135^o=135\frac{\pi}{180}=\frac{3\pi}{4}[/tex]Thus, we have two solutions:
[tex]\begin{gathered} \frac{x}{4}=\frac{\pi}{4} \\ x=\pi \\ And: \\ \frac{x}{4}=\frac{3\pi}{4} \\ x=3\pi \end{gathered}[/tex]Both solutions point to the same terminal angle, so we only have one solution in the first rotation of the angle:
x = π
Since it's required to find the solution for all the real numbers, we must account for all the possible angles in any number of rotations clockwise or counterclockwise as follows:
x = π + 2kπ
Where k is an integer number. For example, for k = 1, we have the already-found solution above x = 3π
Please help if you can. I will only accept answers with work shown. Will give Brainliest.
Initial subscribers: 285
Increase rate : 75 % = 75/100 = 0.75 (decimal form)
years passed = 1994-1985 = 9 years
Apply the formula:
A = P (1 +r ) ^ t
Where:
A = number of cell phone subscribers after t years
P = initial suscribers
r= increase rate in decimal form
t= years
Replacing:
A = 285 (1 +0.75)^9 = 43,872
1x-5x? please help me !
find the perimeter of the given triangle. round to the nearest tenth
The perimeter of the triangle to the nearest tenth is 13.8 units.
How to find the perimeter of a triangle?The perimeter of a triangle is the sum of the whole sides of the triangle.
Therefore, let's find the perimeter of the triangle.
let's find the two missing sides of the triangle as follows;
tan 18 = opposite / adjacent
tan 18 = y / 5.8
y = 5.8 tan 18
y = 1.88453423815
y = 1.88
cos 18 = adjacent / hypotenuse
cos 18 = 5.8 / x
x = 5.8 / cos 18
x = 6.09848421123
x = 6.09
Therefore,
perimeter of the triangle = 5.8 + 1.9 + 6.1
perimeter of the triangle = 13.8 units
learn more on perimeter here: https://brainly.com/question/25617803
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Solve Step 3 onlyTherefore, the solutions of the original equation are the following. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)
ANSWER:
[tex]x=\pi n, \frac{3\pi}{2}+2\pi n[/tex]EXPLANATION"
Given:
[tex]\sin x(\sin x+1)=0[/tex]Having solved Step 1 and Step 2 as seen above, we can go ahead and write the solutions of the equation as seen below;
[tex]\begin{gathered} If\text{ }\sin x=0 \\ \therefore x=\pi \\ \\ If\text{ }\sin x=-1 \\ then\text{ }x=\frac{3\pi}{2} \\ \\ So\text{ }the\text{ }solution\text{ }will\text{ }be; \\ x=\pi n,\frac{3\pi}{2}+2\pi n \end{gathered}[/tex]If a student got 10 answers out of 15 what’s the percent?
To calculate the percentage we have to write a simple fraction like this:
percentage = number of answers / total of questions
percentage = 10 / 15
percentage = 2 / 3
percentage = 0.667
Now, we have to multiply the result by 100:
percentage = 0.667 x 100
percentage = 66.7%
Answer: 66.7%
The legs of a right triangle measure 29 centimeters and 95 centimeters. How long is the hypotenuse in centimeters?
In this question, the two legs of a right angle triangle are:
29 centimeters and 95 centimetres
To find the hypotenuse, let's use Pythagoras Theorem.
[tex]c^2=a^2+b^2[/tex]where ,
a = 29 centimeters
b = 95 centimeters
c = hypotenuse
Therefore,
[tex]c^2=29^2+95^2[/tex][tex]c^2\text{ = 841 + 9025}[/tex][tex]c^2\text{ = 9866}[/tex]Now take the square root of both sides
[tex]\sqrt{c^2\text{ = }}\sqrt{9866}[/tex][tex]c\text{ = 99.327}[/tex]The hypotenus in centimeter is 99.3 centimeters
Which of the following is NOT a level of measurement?Choose the correct answer below.A) OrdinalB) NominalC) RatioD)Quantitative
Given:
A) Ordinal
B) Nominal
C) Ratio
D)Quantitative
Required:
We want to find that Which of the given is NOT a level of measuremen
Explanation:
Levels of Measurement Nominal, Ordinal, Interval and Ratio
but the Quantitative is not the Levels of Measurement because it is
Solve for x. I think u have to do a portion I’m not sure
Answer:
Explanation:
Based on the given figure, we can form similar triangles:
Triangle 1:
Triangle 2:
To solve for the value of x, we use ratio.
[tex]\begin{gathered} \frac{10}{6}=\frac{15}{x} \\ \text{Simplify and rearrange} \\ x=\frac{(15)(6)}{10} \\ x=\frac{90}{10} \\ \text{Calculate} \\ x=9 \end{gathered}[/tex]Therefore, the value of x is 9.
Ms. Friedman and Mrs. Elliot both teachsixth grade math. They share a storagecloset. What is the total area of both roomsand the storage closet?
The two classrooms are identical in length and width. On the other hand, the dimensions of the storage closet are
[tex](40-34)\times(36-30)=6\times6[/tex]The shape of both classrooms and the storage closet is rectangular; therefore, their areas are
[tex]\begin{gathered} A_{\text{rectangle}}=l\cdot w\to length\cdot width_{} \\ \Rightarrow A_{\text{Friedman}}=40\cdot36 \\ _{}A_{\text{Elliot}}=40\cdot36 \\ A_{storage}=6\cdot6 \\ \end{gathered}[/tex]Simplifying,
[tex]\begin{gathered} \Rightarrow A_{\text{storage}}=36ft^2 \\ \Rightarrow A_{\text{Friedman}}=A_{\text{Elliot}}=1440ft^2 \end{gathered}[/tex]Finally, the total area of the compound is
[tex]\begin{gathered} A_{\text{total}}=A_{\text{Friedman}}+A_{\text{Elliot}}-A_{\text{storage}} \\ \Rightarrow A_{\text{total}}=2\cdot1440-36=2844 \end{gathered}[/tex]Thus, the total area of the two classrooms plus the closet is 2844ft^2
Then,
If the side ratio is 4:17, the the area ratio is
The Solution:
Given the side ratio below:
[tex]4\colon17[/tex]We are asked to find the area ratio of the figures being compared.
While the ratio of sides is linear, the ratio of area is square.
This means that if:
[tex]\begin{gathered} \text{ side ratio =4:17} \\ \text{Then it follows that} \\ \text{area ratio will be} \\ \text{ 4}^2\colon17^2=16\colon289 \end{gathered}[/tex]Therefore, the correct answer is [ 16:289 ]
Find the sum of 5 even positive integers
sum of 5 even positive integers
[tex]n+(n+2)+(n+4)+(n+6)+(n+8)[/tex]here, n is the first even number,
let's simplify this,
[tex]\begin{gathered} =n+n+2+n+4+n+6+n+8 \\ =5n+20 \end{gathered}[/tex]Thus the expression to find the sum of 5 consecutive even positive integers is, 5*n + 20 , where n is the 1st even positive integer.
let's use it when n = 2 or to sum 2, 4, 6, 8 and 10
[tex]5*2+20=10+20=30[/tex]which is the same as,
[tex]2+4+6+8+10=30[/tex]Two birds spot a cat trying to jump up to their cage Find the angle of depression of the cat.
Step 1
Draw the triangle for clarity
From the diagram above it is clear, the angle of depression is equal to the angle of elevation since both angles are alternate interior angles. Therefore, we can go ahead to find the angle of elevation which is equal to the angle of depression.
Step 2
Find the angle of depression using SohCahToa
To find this angle we will use the ratio Cah written as
[tex]\begin{gathered} \cos x=\frac{adjacent}{\text{hypotenuse}} \\ \text{adjacent}=4ft \\ \text{hypotenuse}=5ft \end{gathered}[/tex][tex]\begin{gathered} \cos x=\frac{4}{5} \\ x=\cos ^{-1}(\frac{4}{5}) \\ x=36.86989765^{\circ}_{} \\ x\approx36.9^{\circ}\text{ to 1 decimal places} \end{gathered}[/tex]Hence the angle of depression of the cat, x to 1 decimal place = 36.9°
The base of a triangle is given by a number, x (metres). The height of the triangle is ten metres less than the product of two and the number. The area of the triangle is equal to the product of seven and the base length.
According to the question the base of the triangle is x, the height is ten less than the product of two and x, this is 2x-10. The area of the triangle is the product of seven and the base, this is 7x.
The area of a triangle is given by:
[tex]A=\frac{b\cdot h}{2}[/tex]Replace each variable for the given expressions:
[tex]\begin{gathered} 7x=\frac{x\cdot(2x-10)}{2} \\ 7x=\frac{2x^2-10x}{2} \\ 7x=x^2-5x \\ 7=x-5 \\ x=7+5 \\ x=12 \end{gathered}[/tex]x has a value of 12.
(b)Dan leaves his house on his bike. He rides at a constant speed until he reaches a lemonade stand, where he parks his bike and takes a rest. Then he turns around and bikes home as fast as he can.
Answer:
The correct answer is the second graph.
Explanation:
Dan leaves his house at a constant speed. Then, the time starts counting, and his graph is a line that starts in (0, 0)
Then, he stops, we can see this part in the graph constant. Because he is not moving, the distance from his house remains the same.
Finally, goes back and we can this as a line. Since he is going at a faster speed, the line is more steep.
This is what we can see in the second graph