Answer:
Your ans is. a12 = 47/12
Step-by-step explanation:
First, you need to find if the series has a common ratio or a common difference between each term. Based from observation, there is a common difference of 1/3 so the series is an arithmetic series.
The solution for this problem goes like this
an=a1+(n-1)d
a12=1/n+(12-1)(1/3)
a12=47/12
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Tysm
James bought 12 cookies and ate 3 of them. He ate ____% of the cookies. (Make sure to enter the answer using numbers only. Do not enter special characters such as the percent symbol.)
Answer:
25Step-by-step explanation:
Total cookies = 12
Ate = 3 cookies
Now,
Percentage of the cookies that James are:
[tex] \frac{3}{12} \times 100 \: percent[/tex]
Calculate:
[tex] = 25 \: percent[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
answer is 25
Step-by-step explanation:
Determine an expression for the perimeter of the following shape. I need a step by step solution pleaseeeee:)
Answer:
The perimeter of the figure is: 8x + 34.
Step-by-step explanation:
The perimeter of a shape is the sum of the length of all its sides. In this case there is one side missing, we need to find its length. To do that we will have to use Pythagora's theorem, because we will create a right triangle as shown in the attached picture. Where a, b and c are the sides of the right triangle. We can determine the lengths of a and c. If we pay close attention to the figure we will realize that a is:
[tex]a = 2x + 5 - 2x = 5[/tex]
While c is:
[tex]c = 2(x + 7) - (x + 5) - (x - 3)\\c = 2x + 14 -x - 5 -x + 3\\c = 2x - 2x + 12\\c = 12[/tex]
We can now apply Pythagora's theorem:
[tex]b^2 = a^2 + c^2\\b^2 = 5^2 + 12^2\\b^2 = 25 + 144\\b = 13[/tex]
With this we can sum all the sides and calculate the perimeter of the shape.
[tex]2x + 5 + x - 3 + 2x + x + 5 + 13 + 2(x + 7)\\2x + x + 2x + x + 2x + 5 - 3 + 5 + 13 + 14\\8x + 34[/tex]
Two factory plants are making TV panels. Yesterday, Plant A produced 5000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 450 defective panels
Answer:
10,000 panels
Step-by-step explanation:
A TV panel is being produced by two factory plants
Plant A produced 5000 fewer panels than plant B
Let a represent the number of panels produced by plant A and b represent the number of panels produced by plant B
a= b-5000............equation 1
5% of the panels from plant A were defective
= 5/100
= 0.05
2% of the panels from plant B were defective
= 2/100
= 0.02
The total defective panels of both plants is 450
0.05a + 0.02b= 450..............equation 2
Substitute b-5000 for a in equation 2
0.05(b-5000) + 0.02b= 450
0.05b - 250 + 0.02b= 450
Collect the like terms
0.05b+0.02b= 450+250
0.07b= 700
Divide both side by the coefficient of b which is 0.07
0.07 b/0.07= 700/0.07
b= 10,000
Hence plant B produced 10,000 panels
What is P(A|B)?
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
What is P(A|B)? 
A.Not enough information
B.0.50 
C.0.10 
D.0.20
Answer:
50
Step-by-step explanation:
The value of P(A|B) = 0.50 which is correct option(B)
What is independent events?
Independent events is defined as an event that is not affected by other events.
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
P(A|B) = P(A∩B)/P(B)
P(A|B) = P(A).P(B)/P(B)
P(A|B) = P(A)
Substitute the value of P(A) = 0.50,
P(A|B) = 0.50
Hence, the value of P(A|B) = 0.50
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need help a s a p HURRYYYYY
Step-by-step explanation:
v= 4/3πr³
4/3×314/100×8×8×8
•
= 2,143.573
a map is drawn to a scale of 1 cm to 250 cm.
(a) an airport has an area of 240 cm² on the map. find its actual area in km².
Answer:
0.0015 km².
Step-by-step explanation:
It is given that a map is drawn to a scale of 1 cm to 250 cm.
[tex]1\ cm\times 1\ cm=250\ cm\times 250\ cm[/tex]
[tex]1\ cm^2=62500\ cm^2[/tex]
It is given that an airport has an area of 240 cm² on the map. So, its actual area is
[tex]Area=240\times 62500\ cm^2[/tex]
[tex]Area=15000000\ cm^2[/tex]
[tex]Area=\dfrac{15000000}{10000000000}\ km^2[/tex]
[tex]Area=0.0015\ cm^2[/tex] [tex][\because 1\ km^2=10000000000\ cm^2][/tex]
Therefore, the area of airport is 0.0015 km².
Denise bought 116 ounces of beans for a bean dip. She bought both 15-ounce cans and 28-ounce cans, and the total number of cans she bought was 6. Which of these systems of equations can be used to determine the number of 15-ounce cans and the number of 28-ounce cans that she bought? Assume x represents the number of 15-ounce cans and y represents the number of 28-ounce cans. x + y = 6. 15 x + 28 y = 116. x + y = 6. 28 x + 15 y = 116. x + y = 116. 15 x + 28 y = 6. x + y = 116. 28 x + 15 y = 6.
Answer:
2 28ounce cans and 4 15ounce cans
Step-by-step explanation:
28+28=56 and 15+15+15+15=60
56+60=116
Answer:
your answer is the second option
Step-by-step explanation:
hey loves!!! PLz help me
Answer:
Hey there!
We must use what we are given, so even though it looks like there might be four isosceles triangles, we are only given CA=CE, so that only allows us to conclude mathematically that there is only 1 isosceles triangle.
Hope this helps :)
BRAINLIEST!!! MATH HELP ME ASAP PLS!!!
Answer:
-0.0062 and 27.5
Step-by-step explanation:
You can write the equation of the line using the 2-point form:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
The given values of the variables are ...
(h, T) = (10000, -34.5) and (15000, -65.5)
Putting these into the formula, we have ...
T = (-65.5 -(-34.5))/(15000 -10000)(h -10000) +(-34.5)
T = -31/5000(h -10000) -34.5
T = -0.0062h +62 -34.5
T = -0.0062h +27.5
The appropriate choice is ...
-0.0062 and 27.5
Find the area of equilateral triangle with side a.
Answer:
[tex]\frac{\sqrt{3} }{4} a^2[/tex]
Step-by-step explanation:
To find the area of an equilateral triangle, we can apply a formula.
[tex]A=\frac{\sqrt{3} }{4} s^2[/tex]
[tex]A= area\\s=side \: length[/tex]
The side length is given a.
Plug a in the formula as the side length.
[tex]A=\frac{\sqrt{3} }{4} a^2[/tex]
Answer:
3 square root over 4 a square
Step-by-step explanation:
please help me answer this question Solve: y − x = 12 y + x = -26 (19, -7). (-7, 1). (7, 19). (-19, -7).
Answer:
(-19 , -7)
Step-by-step explanation:
y - x = 12
y + x = -25 we sum them to get
2y = -14 , y = -7
then we put -7 instead of y in any of the equations:
-7 - x = 12
-x = 19
x = -19,
finally (x , y) is (-19 , -7)
Type the correct answer in each box. Use the graph to complete the given statements. Enter the letters A, B, C, or D in the boxes. (graph below) The function with the lowest output values as x approaches infinity is ____ . The function with the greatest output values as x approaches infinity is ____ .
As x approaches infinity,
The function with the lowest output is graph A
The function with the greatest output is graph B
===========================================================
Explanation:
As the graphs head to the right, they go up forever. However, the growth rate (how fast they go upward) varies. The red straight line (line A) goes up the slowest. The growth rate is the same throughout the entire function. The rate is the slope of the line. In contrast, the purple curve B goes up the fastest as it has the steepest increase among the four graphs. The graph steadily gets steeper as you move to the right.
The exponential graph will grow the fastest compared to a linear one or parabolic one. Graphs B and C are exponential, where graph B has a steeper curve compared to graph C.
Answer: The function with the lowest output values as x approaches infinity is Graph A.
The function with the greatest output values as x approaches infinity is Graph B.
Step-by-step explanation: I can’t give you a step-by-step explanation, but this is right!
Given: AB = BC, AC is ∠ bisector of ∠BAD Prove: BC ∥ AD
Answer:
<BAC ≅ BCA by rule Base angle theorem
Step-by-step explanation:
What we know:
BAC = DAC
BC = BA
ΔBCA is an isosceles so ∠BCA = ∠DCA and ∠BAC
and we found that out by base angle theorem since
Base angle Theorem = Two base angles of a icosceles triangle are equal.
And since ΔBCA is an isoceles then ∠A and ∠C will be equal. And so we can prove BC is a parallel to AD
The proof that BC ∥ AD from the given statements is that;
BC ∥ AD because of the definition of alternate angles
We are given;
AB = BC
AC is ∠ bisector of ∠BAD
Since AC is the angle bisector of ∠BAD, it means that;
∠BAC = ∠DAC (definition of a bisected angle)
Now, since AB = BC, it means that ΔBCA is an isosceles triangle.
Thus; ∠BCA = ∠BAC (base angle theorem)
Now, since ∠BCA = ∠BAC, and ∠BAC = ∠DAC, we can say that;
∠BCA = ∠DAC
This means ∠BCA and ∠DAC are alternate angles. Thus, we can say that AC is the transversal line carrying the two equal angles.
Thus, we can say that BC is parallel to AD as they are the parallel lines cut by the transversal line AC.
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What is the quotient (2x^3 + 3x - 22) / (x-2)
Answer:
The quotient is 2x^2+4x+11
Step-by-step explanation:
Pam works as an office administrator. She spends $7500 of her income on personal expenses each year. If this represents 18% of her salary, how much money does Pam earn in one year? Round your answer to the nearest whole dollar.
Answer:
Her annual salary is approximately $41,667
Step-by-step explanation:
Hello,
This question deals with percentage of a number and it's very easy :)
First of all, get the data and understand what's required of us.
Pam spends $7500 yearly on expenses
But this amount represents 18% of her annual income.
Let her annual income be represented by x
18% = 7500 / x
18÷100 = 7500÷x
cross multiply and solve for x
18 × x = 7500 × 100
18x = 750,000
divide both sides by 18
18x / 18 = 750,000 / 18
x = $41,666.67
x = $41,667
Her annual salary is approximately $41,667
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5
Answer:
The new points after dilation are
(3/2, -3) and (9/2,-3)
Step-by-step explanation:
Here in this question, we want to give the new points of the line segment after it is dilated by a particular scale factor.
What is needed to be done here is to multiply the coordinates of the given line segment by the given scale factor.
Let’s call the positions on the line segment A and B.
Thus we have;
A = (1,-2) and B = (3,-2)
So by dilation, we multiply each of the specific data points by the scale factor and so we have;
A’ = (3/2, -3) and B’= (9/2,-3)
A blueprint for a house has a scale factor n = 10. A wall in the blueprint is 7 in. What is the length of the actual wall?
840 ft.
5.83 in.
70 ft.
5.83 ft.
Answer:
5.83 ft
Step-by-step explanation:
Given that
Scale factor, n = 10
Wall in blueprint = 7 in
To find:
Length of actual wall = ?
Solution:
Whenever a blueprint is created for any house or building, it is made smaller by a scale factor.
Here this factor is 10 times.
That means, the blueprint size is 10 times smaller than that of its actual size.
Or we can say that actual wall of building is 10 times the wall of blueprint.
So, wall of building = 10 [tex]\times[/tex] 7 = 70 inches
Now, we know that 12 inches = 1 ft
1 inch = [tex]\frac{1}{12}\ ft[/tex]
70 inches = [tex]\frac{1}{12}\times 70\ ft = 5.83\ ft[/tex]
so, the answer is Wall of building is 5.83 ft.
A ladder is placed against a tree. The bottom is located 5 feet from the base of the tree and the top of the ladder is 18 feet up the tree. What is the angle created between the ladder and tree? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a degree.
Answer:
The angle created between the ladder and tree is [tex]15.5^{0}[/tex].
Step-by-step explanation:
The required sketch is shown in the attachment to this answer.
Applying the appropriate trigonometric function to the question, we have;
Tan θ = [tex]\frac{Opposite side}{Adjacent side}[/tex]
= [tex]\frac{5}{18}[/tex]
= 0.2777777777
⇒ θ = [tex]Tan^{-1}[/tex] 0.2777777777
= 15.5241
= [tex]15.5^{0}[/tex]
Therefore, the angle created between the ladder and tree is [tex]15.5^{0}[/tex].
Use the rationalized expression from the previous question to
calculate the time, in seconds, that the cliff diver is in free fall.
Assume the acceleration due to gravity, a, is -9.8 m/s2, and the
dive distance, d, is -35 m. The negative numbers indicate the
direction is downward. Round the answer to two decimal places.
Answer:
Time taken (t) = 2.67 s (Approx)
Step-by-step explanation:
Find:
Time taken (t)
Given:
Initial velocity (u) = 0 m/s
Acceleration due to gravity(a) = -9.8 m/s²
Distance (d) = -35 m
Computation:
Using 2nd equation of motion,
d = ut + (1/2)at²
-35 = (0)t + (1/2)(-9.8)t²
-35 = -4.9 (t²)
t² = 7.1428
t = 2.6726
Time taken (t) = 2.67 s (Approx)
Find the length, x,of the third side of the triangle.
====================================================
Explanation:
This is a visual example of the pythagorean theorem. We add the areas of the two squares to get
13+29.25 = 42.25
Then we apply the square root to this to get the value of x, which is the hypotenuse of the right triangle
x = sqrt(42.25) = 6.5
---------
Side note: if you're curious about finding the other lengths of the triangle, apply the square root to those areas. The blue area 29.25 will lead to a side length of approximately sqrt(29.25) = 5.4083269; the red square will follow the same idea.
Answer:
Step-by-step explanation:
area of a square=a²
A=29.25
a=side=√29.25 first square
second square =a=√13
find x(c)
right triangle: a²+b²=c²
(√29.25 )²+(√13)²=c²
29.25+13=c²
c=√(29.25+13)=6.5 unit
Evaluate m²p - p (m - p ) if m= 3 and p = 5
Answer:
55
Step-by-step explanation:
m^2p - p(m - p), if m=3 and p=5.
So we plug those value into the correct space...
(3)^2 (5) - (5) (3 - 5)
9x5 - 5 x (-2)
45 - (-10)
45 + 10
55
Isiah determined that 5a2 is the GCF of the polynomial
a3 – 25a2b5 – 35b4. Is he correct? Explain.
Answer:
No
Step-by-step explanation:
He's not correct because 5a² isn't a factor of a³ or 35b⁴; in order for something to be the GCF of a polynomial, all of the terms must be evenly divisible by it.
Answer:
a^3 – 25a^2b^5 – 35b^4
He is incorrect since the coefficient of the a^3 term is 1, the GCF cannot contain a coefficient of 5. Also, there is no a in all terms, so a^2 is also not a common factor.
On a trip mrs. ahmed drove 188 miles in 4 hours. On the return trip, she took a different route and traveled 197 miles in 4.5 hours. What was the average rate of speed for the trip?
Answer:
45.29 miles per hour
Step-by-step explanation:
Speed is the distance over time. To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.
Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)
Avg. Speed = 45.29 miles per hour
Hence the average rate of speed for the trip was 45.29 miles per hour.
Cheers.
--------------------------------------------------------
Edit: Thanks to Chegsnut36 for calculation correction
Answer:
≅45.29
Step-by-step explanation:
Hey there!
To find the average rate speed we need to add all the same number.
188 + 197 = 385
4 + 4.5 = 8.5
Now to find the average rate we do,
385 ÷ 8.5 ≅ 45.29
Hope this helps :)
Which of the following are identities? Check all that apply.
Answer:
The true answers:
A
B
C
Step-by-step explanation:
A P E X
Part 2: describe the shape of your cross section of a slice of banana at 45° angle to a space draw picture of the sheep. Part 3: describe the shape of a cross sections if you slice banana and half with a cut perpendicular to its base draw a picture of the shape (hint remember to think of a banana a cylinder)
Answer:
Part 2:
The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points
The drawing of the angle cross section of a cylinder representing the banana is attached
Part 3:
When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle
The drawing of the perpendicular cross section of a cylinder representing the banana is
Step-by-step explanation:
Which equation can be used to find the volume of this solid? A triangular prism. The triangular base has a base of 11 inches and height of 7 inches. The height is 9 inches. V = 11 times 9 times 7 V = 11 + 9 + 7 V = StartFraction 7 + 9 over 2 EndFraction + 11 V = StartFraction 7 times 11 over 2 EndFraction times 9
Answer:
V=11*7*9=693
Step-by-step explanation:
V=Bh ( B is the base area ( base*height) , and h is the height of the prism)
find B=base*h
B=11*7=77 in²
V=B*h=77*9=693 in³
The volume of the triangular prism is 174.25 in³.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, the triangular base has a base of 11 inches and height of 7 inches.
The formula for finding the volume of a triangular prism is V = (base area x height) / 2.
In this case, the base area of the triangle can be calculated using the formula A = (1/2)bh, where b is the base length and h is the height.
In this case, b = 11 inches and h = 7 inches, so the base area is A = (1/2)(11)(7) = 38.5 inches squared.
Now that we have the base area, we can calculate the volume of the triangular prism: V = (38.5 inches² x 9 inches) / 2 = 174.25 in³.
Therefore, the volume of the triangular prism is 174.25 in³.
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halla la medida del lado de un cuadrado cuya diagonal es de 14 cm
Answer:
7√2 cm
Step-by-step explanation:
Aquí, estamos interesados en encontrar la longitud del lado de un cuadrado que tiene una longitud diagonal de 14 cm.
Una diagonal es una línea que se extiende desde un borde del cuadrado hasta el otro borde del cuadrado internamente.
Ahora, una diagonal de un cuadrado junto con dos lados de un cuadrado forman un triángulo rectángulo isósceles, siendo la diagonal la hipotenusa de este triángulo rectángulo.
Sabemos que los lados de un cuadrado tienen la misma longitud y, por lo tanto, llamemos a este lado desconocido x cm.
Matemáticamente, según el teorema de Pitágoras, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los otros dos lados.
Por lo tanto, tenemos;
14 ^ 2 = x ^ 2 + x ^ 2
196 = 2x ^ 2
dividir ambos lados por 2
98 = x ^ 2 x = √98
x = √ (49 * 2)
x = 7√2 cm
Por lo tanto, la longitud del lado del cuadrado es de 7√2 cm
simultaneous equations 2x + y = 21 x - y = 6
Step-by-step explanation:
this is substitution method
Answer:
2x + y = 21
+
x - y = 6
_________
3x = 27
x = 27 ÷ 3
x= 9
x - y = 6
9 - y = 6
9 - 6 = y
3 = y
Therefore, x= 9 and y = 3
Solve by the quadratic formula: 3x2 - 4x + 1 =0
Answer:
x=1.75
Step-by-step explanation:
3*2-4x+1=0 subtract 1 from both sides
3*2-4x=-1 multiply 3 and 2
6-4x=-1 Subtract 6 from both sides
-4x=-7 divide both sides by -4
x=1.75
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Solve each problem below. Show all working in the space provided.
1. A square shed measures 8m 35cm along each side. Find the perimeter of th
shed.
Answer:
Answer:
33m 40cm.
Step-by-step explanation:
One side of the shed measures 8 meters and 35 centimetres, which is 800 + 35 = 835 centimetres.
Since the shed is a square, all side lengths are 835 centimetres long. So, the perimeter is 835 * 4 = 3,340 centimetres. That means that the perimeter is 33 meters and 40 centimetres.
Hope this helps!