3 hours = 3 x 60 = 180 min, then
40 people ---> 20 min
x ----------------> 180 min
[tex]\begin{gathered} x\times20=40\times180 \\ 20x=7200 \\ \frac{20x}{20}=\frac{7200}{20} \\ x=360 \end{gathered}[/tex]answer 1: 360 people in 3 hours
[tex]\frac{360}{3}=120[/tex]answer 2: 120 people per hour
Evaluate the following expression.x³ when x = 5
Given x^3, set x=5 and find the corresponding value, as shown below
[tex]\begin{gathered} x=5 \\ \Rightarrow x^3=5^3=5*5*5=25*5=125 \end{gathered}[/tex]Thus, the answer is 125A triangle has angles that are 38º and 47º. Find the measure of the third angle. 177 ° 95° 133 °85 °
hello,
As we know, a triangule has 3 angles and the sum of them must be equal to 180º. So, let's calculate the question:
38 + 47 + x = 180
85 + x = 180
x = 180 - 85
x = 95º
the volume of prism A is 144^3 if the base is 24^2 what is the height of prism A?
Answer
Height of prism A = 6 units
Explanation
The volume of a prism is given as the product of the area of a face that occurs on two sides of the prism and the distance between the two faces.
In the case of this face being a base, the volume of the prism is given as
Volume = (Area of Base) × (Perpendicular height)
Volume = 144 m³
Area of base = 24 m²
Perpendicular height = h = ?
Volume = (Area of Base) × (Perpendicular height)
144 = (24) × (h)
144 = 24h
We can rewrite this as
24h = 144
Divide both sides by 24
(24h/24) = (144/24)
h = 6 units
Hope this Helps!!!
GIVING 100 POINTS!!
1.) Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 115.2°.
A) 244.8°
B) 64.8°
C) 25.2°
D) 11.5°
2. Find the sum of the interior angles of a 22-sided polygon.
A) 1,980°
B) 2,160°
C) 3,360°
D) 3,600°
HELP! ME PLS!! TWO QUESTIONS!
Answer:
Step-by-step explanation:
1. The answer is C because 180-115.2=64.8
2. The answer is D.
Please give me brainliest!
Answer:
1. C
2. D
Step-by-step explanation:
Because
5. Is X-1 a factor of x^5+2x^2-1?No, because f(1) = 2.Yes, because f(1) = 3.No, because f(1) = 0.Yes, because f(1) = 0.
We want to find if x-1 is a factor of
[tex]f(x)=x^5+2x^2-1[/tex]In order to verify that, we must know the last number of the synthetic division of the polynomial divided by x - 1. If it is zero then it is a factor, and if it is not zero then it is not a factor
If we replace x = 1 in the equation we will find that number:
[tex]\begin{gathered} f(x)=x^5+2x^2-1 \\ f(1)=1^5+2\cdot1^2-1 \\ f(1)=1^{}+2^{}-1 \\ f(1)=2 \end{gathered}[/tex]Then the residual of the polynomial divided by x - 1 is 2, then x - 1 is NOT a factor.
Answer: A No, because f(1) = 2.What is the definition of function?Hos inputs andoutputsInputs haveEvery input hosonly ONE outputxrches andy-wolvesdifferent outputsevery time
The definition of function is
What is the length of side s of the square shown below?45°6S90°A. 2.B. 6C. 3D. 5.2E. 3.2F. .6
The diagram shows a square with one side marked as s, while the diagonal that cuts across measures 6 units.
The diagonal results in a right angled triangle with two sides measuring 45 degrees and one side measuring 90 degrees. Now that we have a right angled with one angle, and two sides (one is given as 6, and one is unknown), we now calculate side s as follows;
[tex]\begin{gathered} \cos 45=\frac{\text{adj}}{\text{hyp}} \\ We\text{ use the ratio for cosine because the sides shown are the} \\ \text{adjacent (between the right angle and the reference angle) and} \\ \text{hypotenuse (facing the right angle)} \\ \cos 45=\frac{s}{6} \\ \cos 45=\frac{1}{\sqrt[]{2}} \\ \text{Therefore,} \\ \frac{1}{\sqrt[]{2}}=\frac{s}{6} \\ \text{Cross multiply and you have} \\ \frac{6}{\sqrt[]{2}}=s \\ \text{Rationalize the expression and you have} \\ 3\sqrt[]{2}=s \\ \text{Therefore} \\ s=3\sqrt[]{2} \end{gathered}[/tex]The correct answer is option E
Convert the following mixed number to improper fraction10 /2/57 3/20
The question asks us to convert mixed fractions to improper fraction.
The first Mixed fraction is:
[tex]\begin{gathered} 10\frac{2}{5} \\ \text{whole number = 10} \\ \text{ numerator = 2} \\ \text{ denominator = 5} \end{gathered}[/tex]In order to convert this into an improper fraction, we need to follow some steps:
1. Multiply the denominator by the whole number.
2. Add the result of the multiplication in step 1 to the numerator.
3. The result from step 2 is the new numerator and use the current denominator as the new denominator.
Let us now apply these steps to answer the question
1. Multiply the denominator by the whole number.
[tex]5\times10=50[/tex]2. Add the result of the multiplication in step 1 to the numerator.
[tex]50+2=52[/tex]3. The result from step 2 is the new numerator and use the current denominator as the new denominator.
[tex]\begin{gathered} \text{new numerator = 52} \\ \text{new denominator = 5} \\ \therefore\frac{52}{5} \end{gathered}[/tex]Therefore, the answer is:
[tex]10\frac{2}{5}=\frac{52}{5}[/tex]Now, let us use the same rules for the next question.
[tex]7\frac{3}{20}[/tex]1. Multiply the denominator by the whole number.
[tex]7\times20=140[/tex]2. Add the result of the multiplication in step 1 to the numerator.
[tex]140+3=143[/tex]3. The result from step 2 is the new numerator and use the current denominator as the new denominator.
[tex]\begin{gathered} \text{new numerator= 143} \\ \text{new denominator = 20} \\ \therefore\frac{143}{20} \end{gathered}[/tex]Therefore, the final answer is:
[tex]7\frac{3}{20}=\frac{143}{20}[/tex]Find the measure of each angle in the diagram.
Answer:
10y+7x+4+4×-22+3y+11
10y+3y+7x+4x+4-22+11
13y+11x-9
15 percent of a certain company's life insurance policy holders are smokers. For each nonsmoker the probability of dying during the year is 0.011. For each smoker the probability of dying during the year is 0.04. Find the probability that a policy holder who died last year was a smoker.
Percentage of Smoker Policy Holders = 15% / 100% = 0.15
Probability of Smokers Dying = 0.04
Let's substitute the values to the equation, we get,
[tex]\text{ P = (0.15)(0.04) = 0.006}[/tex]The probability that a policy holder who died last year was a smoker = 0.006
Evaluate: 4+8/2 x (6 - 3)163325
We have to evaluate the expression:
[tex]\begin{gathered} 4+\frac{8\cdot(6-3)}{2}_{} \\ 4+\frac{8\cdot3}{2} \\ 4+\frac{24}{2} \\ 4+12 \\ 16 \end{gathered}[/tex]To solve this, we have to solve the operations in this order:
- First, the operations within the parenthesis.
- Second, the multiplications and quotients.
- Lastly, the additions and substractions.
Answer: 16
What do the expanded form and a place- value chart tell you about a number such as 25,049?How are they alike and different
The expanded form of a number is written out in such a way that you would be able to see the math value of individual digits.
The number 25,049 which reads "twenty five thousand and forty nine," can be written in expanded form as follows;
2 x 10000 = 20,000
5 x 1000 = 5,000
0 x 100 = 0
4 x 10 = 40
9 x 1 = 9
So, as you can see the expanded form shows that the digit 2 (for example) in this number has a value of 20,000.
The place value chart groups the number in threes starting from the right to the left. That is, you count three numbers from the end (right hand side) insert a coma, and take the next three set of digits and so on. You can now tell the value of each digit by starting from the left (the begining) to the right (the end). Usually starting with billions, the chart now tells you the value of each digit. So in this question, you can read from left to right and by using the expanded form, you can tell the value of the 2, the 5, and so on till the last digit.
They are alike because the expanded form helps you determine the actual value of each digit without mistake, and the place value also tells you which number carries what value.
They are different because an expanded form gives you details of how each number gets its place value, while the place value chart simply tells you the value of each digit simply by arranging and inserting comas.
Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given interval.
Given:
[tex]f(x)=10x^4-4x^2+5x-1;\lbrack-2,0\rbrack[/tex]Using the intermediate value theorem,
[tex]\begin{gathered} f(x)=10x^4-4x^2+5x-1 \\ f(-2)=10(-2)^4-4(-2)^2+5(-2)-1 \\ f(-2)=160-16-10-1=133 \\ \text{and} \\ f(0)=10(0)^4-4(0)^2+5(0)-1=-1 \end{gathered}[/tex]So, we have find value c between [-2,0].
[tex]\begin{gathered} f(x)=0 \\ 10x^4-4x^2+5x-1=0 \\ \Rightarrow x=-1\text{ it satisfies the equation} \\ \text{Also, -1}\in\lbrack-2,0\rbrack \end{gathered}[/tex]It shows that, the above polynomial function has zero in the given interval.
Also, the value of f(-2) = 133
Yuson must complete 30 hours of community Service. She does two hours each day. Write a linear equation to represent the hours she has left after X days.
Yuson must complete 30 hours of community service.
She does two hours each day.
We are asked to write a linear equation to represent the hours she has left after x days.
We can write the following linear equation
[tex]30-2x=0[/tex]Where 30 represents the total hours of community service that Yuson has to complete.
2 represents the hours she works each day.
x represents the days.
We can also solve this equation to find how many days will it take her to complete the community service.
Select the values that make the inequality m≥7 true.
(Numbers written in order from least to greatest going across.)
Step-by-step explanation:
every number greater than or equal to 7.
just as the expression says.
are we taking only about integer values ?
so,
7, 8, 9, 10, ... +infinity
if we aim for radical or real values, then starting with 7 everything between these numbers.
the interval definition is
[7, +infinity)
please note the different brackets.
"[" or "]" means the interval end value is included.
"(" or ")" means the interval end value is excluded.
which is the normal thing for infinity, because infinity is only a concept and never a number. so, it cannot be included.
Hi I just wanted you to check over my work to let me know if I did it correct
Answer:
Hello, Which part would you like to have checked?
I can't seem to make out your work from that of the assignment.
Step-by-step explanation:
Just let me know, here to help!
What is the first step to solve this equation: 5m + 10= 7m + 4A: subtract 5m to both sides B: add 5m to both sides C: divide by 5 to both sides D: multiply by 5 to both sides
We are given the linear equation
[tex]5m+10=7m+4[/tex]If we subtract 5m to both sides we get
[tex]5m+10-5m=7m+4-5m[/tex]Simplifying
[tex]10=2m+4[/tex]which is one step closer to the solution, therefore the answer is A.
According to the diagram, an 8-foot-tall statue casts a shadow on the ground that is 15 feet in length. Based on this information, which trigonometric ratio has the value 8/15 ?A. cos CB. tan BC. cos BD. tan C
the right optio is tan C because...
[tex]undefined[/tex]This is a practice assessment that will not be graded! Just need help finding this answer to understand it overall
The general structure of the equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
h is the x-coordinate of the center of the circle
k is the y-coordinate of the center of the circle
r is the radius of the circle.
Note that the equation has minus signs inside the parentheses, this means that the sign of the coordinates is the opposite as the one shows on the equation.
The first step is to identify the coordinates of the center of the circle in each equation as well as the radius:
Equation 1:
[tex](x-3)^2+(y+2)^2=9[/tex]The x-coordinate of the center is the value inside the first parentheses: h= 3
The y-coordinate of the center is the value inside the second parentheses: k= -2
[tex]center\colon(3,-2)[/tex]To determine the radius you have to calculate the square root of the last number of the equation:
[tex]\begin{gathered} r^2=9 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Use the same logic for the other three equations:
Equation 2:
[tex](x-3)^2+(y-2)^2=16[/tex]h=3
k=2
[tex]\text{center:(3,2)}[/tex]Radius:
[tex]\begin{gathered} r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}[/tex]Equation 3
[tex](x+3)^2+(y+2)^2=16[/tex]h=-3
k=-2
[tex]\text{center:(-3,-2)}[/tex]Radius:
[tex]\begin{gathered} r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}[/tex]Equation 4
[tex](x-3)^2+(y-2)^2=9[/tex]h=3
k=2
[tex]\text{center:(3,2)}[/tex]Radius:
[tex]\begin{gathered} r^2=9 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Next, you have to determine the center and the radius of each graph:
Circle 1:
Has a radius with a length of 4 units and center (3,2), the equation that corresponds to this circle is the second equation.
Circle 2:
Has a radius with a length of 4 units and the center at (-3,-2), the equation that corresponds to this circle is the third equation.
Circle 3:
Has a radius with a length of 3 units and a center at (3,2), the equation that corresponds to this circle is the fourth equation.
Circle 4:
Has a radius with a length of 3 units and center at (3,-2), the equation that corresponds to this graph is the first equation.
m = y2-yi=X2-X1Find the slope of the line that passesthrough these two points.(6,4)m = [?](2, -4)-
The slope between two points (x1,y1) and (x2,y2) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case we have the points (2,-4) and (6,4), then:
[tex]\begin{gathered} m=\frac{4-(-4)}{6-2} \\ m=\frac{4+4}{4} \\ m=\frac{8}{4} \\ m=2 \end{gathered}[/tex]Therefore, the slope is 2
Solve the following absolute value inequality. Express your answer in interval notation.
Okay, here we have this:
We need to solve the following inequality, let's do it:
[tex]\begin{gathered} 3\mleft|5-y\mright|\le\: -6 \\ \mleft|5-y\mright|\le\: -2 \end{gathered}[/tex]And considering that the absolute value cannot be less than zero, it means that the inequality has no solution in the set of reals.
ine TrackerWhat additional piece of information is needed in order to say thatthese two triangles are congruent by AAS postulate?BO BC DEO AB DEO BC EFO AB DF
Answer
Option B is correct.
AB ≅ DE
Explanation
The key to two triangles being similar according to AAS is that they have two angles and an excluded side in common.
An excluded side does not reside between the two congruent angles.
So, for these two triangles to be congruent according to AAS,
Angle C = Angle F
Angle B = Angle E
And
Side AB ≅ Side DE
Hope this Helps!!!
A Ferris wheel with a 200-foot diameter is spinning at a rate of 10 miles per hour. Find the angular speed of the wheel in radians per minute.
1) Gathering the data from the question:
Diameter = 200'
Spinning at 10mph
2) Let's convert the units to start working through that:
[tex]\begin{gathered} m------ft \\ 1------5280 \\ -- \\ 1h=60\min \end{gathered}[/tex]So, 1 mile=5280 ft and 1 hour = 60minutes. Then we can convert:
[tex]\frac{10m}{60}=\frac{10\times5280}{60}=\frac{880ft}{\min }[/tex]2.2) Since we have the diameter, then we can state the radius of this Ferris Wheel is 100 ft. Let's plug into the Circumference formula to get the circumference of the Ferris Wheel:
[tex]\begin{gathered} C=2\pi r \\ C=2\pi\cdot100 \\ C=200\pi \end{gathered}[/tex]2.3) We can find the angular velocity since we have the speed and the Circumference. Note that the angular velocity is given as quotient between the speed and the circumference:
[tex]\frac{880}{200\pi}=\frac{22}{5\pi}[/tex]Note that this is given in revolutions per minute. And 1 revolution corresponds to one lap (2π radians). So we need another final conversion for the unit wanted for the question is radians per minute.
[tex]\frac{22}{5\pi}\times2\pi=\frac{44}{5}=8.8[/tex]3) Thus the answer is:
[tex]8.8\: radians\: per\: minute[/tex]Six office desks that are 7 1/12 feet long are to be placed together on a wall that is 42 7/12 feet long. Will they fit on the wall? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes, if no more than a total of foot is needed for spacing between desks. (Type an integer or a simplified fraction.) B. No, they do not all fit along the wall.
Answer:
[tex]\text{Yes, If no more than a total of }\frac{1}{12}foot\text{ is needed for spacing between desks}[/tex]Explanation:
Given that six office desks that are 7 1/12 feet long are to be placed together.
The length of the six desks is;
[tex]\begin{gathered} 6\times7\frac{1}{12} \\ =6\times7+6\times\frac{1}{12} \\ =42\frac{6}{12} \end{gathered}[/tex]Given that the wall is 42 7/12 feet long.
Then the length of the six desks is shorter than the length of the wall.
[tex]42\frac{7}{12}-42\frac{6}{12}=\frac{1}{12}[/tex]Therefore, it will fit on the wall if no more than a total of 1/12 foot is needed for spacing between desks.
[tex]\text{Yes, If no more than a total of }\frac{1}{12}foot\text{ is needed for spacing between desks}[/tex]Which of the following is the graph of the following system of equations? { 2x - 3y>12 {y< -1 x + 5 2
SOLUTION
The graph of the inequality
[tex]\begin{cases}2x-3y\ge12{} \\ y<-\frac{1}{2}x+5\end{cases}[/tex]is shown below
The darkest part is the required region
Comparing with the options,
the answer is the graph below
find the exact value of cosine Pi / 3 express your answer with a rational denominator
it is given that,
the expression is
cosine Pi/3
we know that
so,
[tex]\cos \frac{\pi}{3}=\cos \frac{180}{3}=\cos 60=\frac{1}{2}[/tex]thus, the answer is 1/2
What is the measure of angle J in the triangle below? *Hint: Law of Sines*
SOLUTION:
Using the sine rules;
The equations developed;
[tex]\frac{15}{sin102}=\frac{12}{sinJ}[/tex]Making sinJ the subject;
[tex]\begin{gathered} sinJ=\frac{12sin102}{15} \\ sinJ=0.7825 \\ J=51.49^o \end{gathered}[/tex]Thus, the angle is 51.5 degrees.
Hello, May I please get some assistance with this homework question? I posted an image below Q2
Solving (a)
The two functions we have are:
[tex]\begin{gathered} f(x)=3x+3 \\ g(x)=x^2 \end{gathered}[/tex]We are asked to find the composite function:
[tex](f\circ g)(x)[/tex]Step 1. The definition of a composite function is:
[tex](h\circ k)(x)=h(k(x))[/tex]In this case:
[tex](f\circ g)(x)=f(g(x))[/tex]This means to plug the g(x) expression into the value of x of the f(x) function.
Step 2. Substituitng g(x) as the value for x in f(x):
[tex](f\circ g)(x)=f(g(x))=4(x^2)+3[/tex]Simplifying:
[tex](f\circ g)(x)=\boxed{4x^2+3}[/tex]Step 3. We also need to find the domain of this composite function.
The domain of a function is the possible values that the x-variable can take. In this case, there would be no issues with any x value that we plug as the x-value. Therefore, the domain is all real numbers.
The domain of fog is all real numbers.
Answer:
[tex](f\circ g)(x)=\boxed{4x^2+3}[/tex]The domain of fog is all real numbers.
train moves at a constant speed of 8 miles every 6 minutes. Fill in the table below to show how far the train travels according to differentmounts of time.Time (minutes)Distance (miles)31560
we have the following:
speed 8 miles every 6 minutes:
[tex]s=\frac{8}{6}=1.34[/tex]therefore, the speed is 1.34 mi/m, now to complete it would be:
[tex]\begin{gathered} d=s\cdot t \\ d1=1.34\cdot3=4 \\ d2=1.34\cdot15=20 \\ d3=1.34\cdot60=80 \end{gathered}[/tex]therefore, the answer is:
Time (minutes) Distance (miles)
3 4
15 20
60 80
Find the surface area of the giving prism round to the nearest 10
The surface area of the given prism is the sum of areas of all sides.
From the given figure, we have :
2 Triangles with a base of 9 ft and a height of 7.6 ft
1 rectangle with a length of 13 ft and a width of 10 ft
1 rectangle with a length of 13 ft and a width of 8 ft
1 rectangle with a length of 13 ft and a width of 9 ft
The formula for the area of a triangle is :
[tex]A=\frac{1}{2}\times Base\times Height[/tex][tex]A=\frac{1}{2}\times9\times7.6[/tex][tex]A=34.2[/tex]Since there are two triangles, the total area of the triangle is :
[tex]A=2\times34.2=68.4[/tex]The formula for the area of the rectangle is :
We can add the three triangles together.
[tex]A=(13\times10)+(13\times8)+(13\times9)[/tex][tex]A=130+104+117[/tex][tex]A=351[/tex]Now we have the areas of the sides, take the sum of these areas to find the surface area.
[tex]\text{Surface Area = 68.4 + 351}[/tex][tex]\text{Surface Area = 419.4 ft\textasciicircum{}2}[/tex]