Answer:
1) 4
2) exponential decay
3) [tex]y = 4(0.8)^x[/tex]
Step-by-step explanation:
1) The initial value or an exponential function is the y-intercept.
Let us consider a standard exponential function of the form y(x) = a•bˣ , if you put in x = 0 (initial value) we get:
y(0) = a•bˣ = a•b⁰ = a•1 = a , so the y-intercept is a , which is called the initial value.
Therefore the y intercept is 4
2) Since the multiplier is greater than 0 and less than one, it is an exponential decay
3) standard exponential function of the form y(x) = a•bˣ, at (0,4),
4 = a(b)⁰
a = 4
b = multiplier = 0.8
Therefore: [tex]y = 4(0.8)^x[/tex]
Bernard is one and half times old as Henry six years ago he was twice as old as Henry how old are the boys now
Answer:
Henry=12, Bernard=18
Step-by-step explanation:
let Henry's age = x
let Bernard's age= 1.5x
according to d passage 6yrs ago x×2=1.5x
mathematically that is (x-6)2=1.5x-6
2x-12=1.5x-6
2x-1.5x=-6+12
0.5x=6
divide both sides by the co-efficient of x which is 0.5 can also be written as ½
there fore x=6÷½
x=Henry's age=12years
1.5x=Bernard's age=12×1.5=18years
What is the value of x in the equation 3 minus 2 x = negative 1.5 x? People say the Answer is 6. What's the work to get the answer?
Answer:
6
Step-by-step explanation:
3-2x=-1.5x
3=2-1.5x
3=0.5x
X=(3÷0.5)=6
Please help will be marked BRAINLIEST!
Answer:
shorter base = 6 yd
longer base = 8 yd
area of playground = 42 yd^2
Step-by-step explanation:
The question tells you that the shorter side is equal to the width, which is 6 yds. The bases of the triangles on either side are 1 yd. Since there are two, add 1 twice to 6 (6+1+1). This gives you 8 yd for the longer base. You're right about the area, just use the trapezoid area formula: 1/2h(a+b).
At a school dance, student tickets cost $5 each and non-student
tickets cost $7 each. The total amount of money earned from ticket
sales equals $1840. If 120 non-student tickets were sold, which
equation could be used to figure out how many student tickets were
sold?
Considering the number of student tickets sold as x.
5x+7*120=1840
5x+840=1840
5x=1840-840
5x=1000
x=1000/5
x=200
200 student tickets were sold.
Can someone please help me it’s for geometry thank you :)
Answer:
QST = 2x= 2*20 = 40°
Step-by-step explanation:
RSQ+QST= RST
we know that RST is 124
So,
84+2x= 124
Bringing 84 to the other side it becomes negative
2x= 124-84
= 40
Therefore,
x= 40/2
= 20 °
Here's your answer :)
Which term describes how to determine if a relation given in a table is a function
A. If none of the output values are repeated, the relation is a function
B. If none of the input values are repeated, the relation is a function
C. If any of the input values are equal to the output values, the relation is a function
D. If all the output values are paired with the same input value, the relation is a function
Answer:
A. If none of the output values are repeated, the relation is a function
Step-by-step explanation:
The reason why A is correct stems from the concept of the vertical line test. If each x-value has their own respective output (y-value), then the relation is a function.
Choice B just states that if none of the x-values are repeated. then the relation is a function. This is not correct because it doesnt follow the vertical line test, which analyzes if any y-values are being repeated
Choice C and D doesnt have any correlation with the vertical line test because an x-value doesnt have to equal a y-value to make the relation a function. Vice versa for any y value being equal to any x-value.
Robin is a competitive archer. Her average arrow is within 6.5 cm of the center of the bullseye. John, Robin's trainer, keeps close records of each of Robin's shots so he can tell if she is improving. The graph below is John's record of Robin's last three arrows, where (0,0) is the center of the bullseye.
Answer:
Arrow C.
Step-by-step explanation:
Out of three arrows, nearest arrow from the origin will be the best arrow.
Ordered pair for arrow A → (-5, 4)
Distance between A and bullseye = [tex]\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2}[/tex]
= [tex]\sqrt{(0+5)^2+(0-4)^2}[/tex]
= [tex]\sqrt{41}[/tex]
= 6.40 units
Ordered pair for arrow B → (5, -5)
Distance between B and bullseye = [tex]\sqrt{(0-5)^2+(0+5)^2}[/tex]
= [tex]5\sqrt{2}[/tex]
= 7.1 units
Ordered pair for arrow C → (-2, -6)
Distance between C and the bullseye = [tex]\sqrt{(0+2)^2+(0+6)^2}[/tex]
= [tex]\sqrt{40}[/tex]
= 6.32 units
Distance between C and the bullseye is the shortest.
Therefore, arrow C will be the best arrow.
Answer:
6.3 cm
Step-by-step explanation:
Please answer if you know..?
Answer:
B→A
Step-by-step explanation:
I'm pretty confident in my answer.
A shopkeeper sold a watch for Rs 810 at 10% loss. How much did he pay to buy the watch ?
Answer:
Rupees 891
Step-by-step explanation:
If you multiply 810 times 0.1 which is the decimal of 10%, you get 81 which you can add to 810 to get 891 which is the price the shopkeeper payed to buy the watch.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Select all the equations where a=8 is a solution.
Choose 3 answers:
A
a+11=15
B
1=8÷a
C
15+a=23
D
42=7a
E
a-5=3
Answer:
B,C, E
Step-by-step explanation:
A
a+11=15
8+11 = 19
false
B
1=8÷a
1 = 8÷8
1=1 true
C
15+a=23
15+8 = 23
23 = 23
true
D
42=7a
42 = 7*8
42 = 56
false
E
a-5=3
8-5 = 3
3=3 true
how do you know if two line segments are perpendicular
A. Their slopes are equal
B. The slope of one is the negative of the slope of the other
C. Their slopes are negative reciprocals
D. Their slopes are reciprocals
Answer: C. Their slopes are negative reciprocals
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other.
The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.
The number of times one needs to use the completely filled cone to completely fill the cylinder with water is
Well, we would find the volume of both the cylinder and the cone.
The formula to find the volume of a cylinder is V = \pi r^{2} h.
The formula to find the volume of a cone is V = \frac{1}{3} \pi r^{2} h.
Now, when using pi (the symbol \pi ), if the problem asks to use the approximate value of pi as 3.14, we'll use 3.14 to represent pi. If the problem asks for the exact answer, then we'll just put the pi sign next to our final answer we've gotten.
We can do both ways to solve with pi. Tho let's solve using the approximate value of pi.
One more thing. When there's an exponent in the problem, (such as r^{2} in the problem), that just means you would multiply the base, (which is r in r^{2} ), by itself the number of times the exponent, (which is the number 2 in r^{2} ), shows. For example, if it was 3^{2} , that would just mean we would multiply 3 times itself twice. So 3^{2} would be the same as 3 times 3, which is 9. When you deal with variables in a problem, (the letters used to represent a value in the equation, such as a, b, c, d, etc.), they're solved in multiple ways. If a number is next to a variable, (for example, 3b), it would mean you are supposed to multiply the number times the variable. If a number is next to parenthesis, that would mean you would multiply the number times the answer from the parenthesis. In formulas, when all the letters and numbers are squished together in one line, that means you would multiply all of them times each other after they're individually solved. In this problem, r = radius and h = height.
So without further-a-do, let's begin! :)
So the question says that the radius of the cylinder is 10 centimeters, and the height is 20 centimeters. According to the formula given above, we would multiply the radius times itself twice, which would be 10 times 10, which equals 100, then multiply it by the height which is 20, so 100 times 20 = 2,000. If we were to find the exact volume, it would be 2,000 with the pi sign next to it, which would be 2,000 \pi . Though, let's find the volume with the approximate value of pi, 3.14. So 2,000 times 3.14 is 6280. The exact volume of the cylinder is 2,000 \pi and the approximate volume is 6280.
Now after we find the volume of the cone, we would need to find out how many times we'd need to use the cone to fill up the cylinder's volume.
To find the volume of the cone, we would do the same as last time. Since the cone's radius is 5 centimeters, and its height is 10 centimeters, we would first multiply the radius times itself twice, which would be 5 times 5, which is 25, then multiply that by the height, which would be 25 times 10, which is 250. The fraction part of the formula means this- the numerator "1" means you would multiply what you have so far times 1, and the denominator "3" means you will divide what you have so far NOW by 3. So 250 times 1 = 250, and 250 divided by 3 = 83.3333333333, though we'd say that answer up to the hundredths place, which would be 83.33. If you need the exact answer, we'd put the pi sign next to it as 83.33 \pi , and you're done.Tho we didn't find the approximate volume of the cone.So we'd trace back to what answer we had before moving on to the step with the fraction \frac{1}{3} . Since we were on 250, we'd multiply that by 3.14, which is 785, and continue with what we did with the fraction. 785 times 1 = 785, and 785 divided by 3 = 261.666666667, and saying the answer up to the hundredths place, the approximate volume of the cone would be 261.66
Now since we know the volume of the cylinder, exact = 2,000 \pi and approximate volume = 6280, this means this is how much of the cylinder should be filled when we use the cone to pour in the water.
We could easily determine this by division.
Finding with the exact volume, you would do 2,000 (from cylinder's volume) divided by 83.33 (from cone's volume), which is 24.0009600384, and since it's not a whole answer, you would move it up a whole number. Why you may ask? Well you can't pour 0.0009600384 of a cone's volume into the cylinder now can you? :P So it would take 25 times of pouring the cone filled with water into the cylinder in order for the cylinder to be full using the exact volumes of both objects.
Now finding with the approximate volumes of both objects, we'd do the same we did last time. The cylinder's volume divided by the cone's volume, which is 6280 divided by 261.66, would be 24.0006114805, and saying the answer up to the hundredths place, 24.00, but for the same reason as the last one when we were using the exact volumes, we'd round 24 up a whole number, so it would approximately take 25 times to fill the cylinder with the cone.
Either way, using exact or approximate volumes, your final answer would be 25 times. =DI hope I helped! ^-^
By calculating the volume of cone and cylinder, we find that one need to 24 times use the completely filled cone to completely fill the cylinder with water.
What is volume of cone and cylinder?
The volume of cylinder is equal to the product of the area of the circular base and the height of the cylinder.
The volume of cone will be equal to one-third of the product of the area of the base and its height.
For a cylinder, the formula is πr²h. For a cone it is 1⁄3πr²h.
Volume of cylinder = π[tex]r^{2}[/tex]h = π * 10* 10 * 20 = 2000π
Volume of cone = [tex]\frac{1}{3}[/tex]*π[tex]r^{2}[/tex]h = 1/3 * π * 5 * 5 * 10 = 250 π/3
Number of times one needs to use the completely filled cone to completely fill the cylinder with water =
= Volume of cylinder/Volume of cone
= 2000π / (250π/3) = 24
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Please help! Correct answer only!
A raffle has 1,000 tickets. One ticket will win a $830 prize. The remaining tickets will win nothing. If you have a ticket, what is the expected payoff?
Answer:
" Expected Payoff " ⇒ $ 0.830
Step-by-step explanation:
Consider the probability of entering 1 ticket out of the 1000 entered;
[tex]Total Tickets Entered - 1000 Tickets,\\Prize Won - 830 Dollars,\\Number of Tickets One Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 1000,\\Proportionality - 1 / 1000 = x / 830, If x = " Expected Payoff ",\\\\1 / 1000 = x / 830 - Cross Multiplication ,\\1000 * x = 830,\\x = 830 / 1000 = 0.830\\\\Conclusion ; x = 0.83[/tex]
Solution ; " Expected Payoff " ⇒ $ 0.830 ( might or might not include 0 at end )
Need help thanks :) The question is down below
Answer:
n=63
x=117
r=63
p=117
w=117
m=117
k=117
Step-by-step explanation:
If you start with the given angle of 63 p would have to be 117 because 180-63 is 117. This would make r 63 because you would use the 117+63 to make a 180 degree angle. w will then be made 117 because it's vertical to p and vertical angles are congruent. we can find x by using corresponding angles. x= k because they are corresponding angles as well. n would be 63 because of k being 117 and because of vertical angles m is 117.
Hope this helps :)
What is the value of n in the equation (2n + 4) + 6 = -9 + 4(2n + 1)?
n =
the answer is just 1.
Answer:
n=2.5
Step-by-step explanation:
(2n + 4) + 6 = -9 + 4(2n + 1)2n+10=-9+8n+42n+10=8n-58n-2n= 10+56n=15n=15/6n=2.5Answer:
The answer is 1.
Step-by-step explanation:
A woman hikes 503 m, turns and jogs 415 m, turns again and runs 365 m returning to her starting point.
What is the area of the triangle
formed by her path?
Round to the nearest tenth.
Answer:
74594.2 m
Step-by-step explanation:
Heron's formula
area=sqrt(p(p-a)(p-b)(p-c)) where p=(a+b+c)/2
[tex]\sqrt{641.5(641.5 - 503)(641.5 -415)(641.5 - 365)}[/tex]The total amount of area of the triangle which she has covered is 74594.17.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
Area of triangle = 1/2 ×base ×height.
Given that A woman hikes 503 m, turns and jogs 415 m, turns again, and runs 365 m returning to her starting point
so the triangle which is made by the woman(no matter what kind of triangle is) has a side as
A = 503m , B = 415m , C = 365m
Now S = (A + B + C)/2
S = (503 + 415 + 365)/2
S = 641.5
Now the area of a triangle is given by
Area = [tex]\sqrt{S(S - A)(S -B)(S - C)}[/tex]
Area = [tex]\sqrt{641.5 (641.5 - 503)(641.5 -415)(641.5 - 365)}[/tex]
Area = 74594.17 hence, the area of the triangle will be this.
For more information about triangle
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Find the length of side AB. Give your answer to 1 decimal place.
Answer:
Length of side AB = 5.6 cm
Step-by-step explanation:
From the figure attached.
In right triangle ABC,
m∠ABC = 62°
m(BC) = 12 cm
By applying Cosine rule in this triangle,
Cos62° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
Cos62°= [tex]\frac{AB}{BC}[/tex]
0.46947 = [tex]\frac{AB}{12}[/tex]
AB = 12 × 0.46947
AB = 5.63
≈ 5.6 cm
Therefore, length of side AB = 5.6 cm
Length of side AB = 5.6 cm.
Calculation of the length of side:Since In right triangle ABC,
m∠ABC = 62°
m(BC) = 12 cm
Here we used the cosine rule
So, it is
[tex]Cos 62 = AB\div BC\\\\0.46974 = AB\div 12[/tex]
So, AB = 5.6 cm
hence, Length of side AB = 5.6 cm.
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Suppose that a particular experiment will have outcome “A” with probability 13 and outcome “B” with probability of 23. If you were to perform this experiment 90 times, approximately how many times would you expect outcome “B” to occur
A basket ball that has a diameter of 20cm is placed in a box so that it touches all inner sides of a box. What is the volume NOT occupied by the ball when it is placed in the box?
Please help me asap
Answer:
3811.21
Step-by-step explanation:
volume of sphere is 4188.79 using the formula for the volume of a sphere.
volume of the box is=20x20x20=8000
8000-4188.79=3811.21
the weights of cars passing over a Bridge have a mean of 3550 lb and a standard deviation of 870 lb. Assume that the weights of the cars passing over the bridge, Lee distributed. Use the empirical rule to estimate the percentage of the cars going over the bridge whose weights are more than 4420 lbs.
Answer:
a. 16%
Step-by-step explanation:
The difference from the mean is ...
(x - µ) = 4420 lb -3550 lb = 870 lb
Then the minimum Z-score of the traffic of interest is ...
(x - µ)/σ = (870 lb)/(870 lb) = 1
__
The "empirical rule" tells you that 68% of a normal distribution is within 1 σ (Z = ±1) of the mean. If 68% is inside that range, then the remaining 32% is outside that range. The normal distribution is symmetrical about the mean, so half that quantity is below Z = -1, and the other half, 16%, is above Z=1.
About 16% of the cars have weights more than 4420 pounds.
I have worked the answer to a which is 301.6 but I’m not too sure how you work out b any help would be much appreciated!
Answer:
188.5 cm^2
Step-by-step explanation:
a) Your volume is correct.
b) The curved surface area of the cone is called the lateral area.
Its formula is:
LA = (pi)rs,
where pi is 3.14159...
r = radius of the base
s = slant height of the cone
Here, r = 6 cm, and s = 10 cm
LA = (3.14159)(6 cm)(10 cm)
LA = 188.5 cm^2
what is the value of x?
Answer:
60 degrees
Step-by-step explanation:
Since the two lines are intersecting, the angles formed by them are vertical angles. Therefore:
2x+24=144
2x=144-24=120
x=120/2=60
Hope this helps!
Step-by-step explanation:
Therefore,
2x+24= 144° [ Vertically positive angles]
Or, 2x= 144-24
Or, 2x= 120
Or, x= 120/2
Therefore, x= 60°
Los lados de un triángulo rectángulo miden 6m, 8m y 10m. respectivamente. ¿Cuánto medirán los catetos de un triángulo semejante al primero si su hipotenusa mide 15m?
Answer: Los catetos medirán 12m y 9m.
Step-by-step explanation:
Bueno, sabemos que los lados de nuestro triangulo son 6m, 8m y 10m.
Podemos usar relaciones trigonométricas para encontrar los ángulos de este triangulo.
Cos(X) = cateto adyacente/hipotenusa
Si tomamos al cateto adyacente como 8m, tenemos:
Cos(X) = 8m/10m
X = Acos(8/10)
Esto nos dice que para que nuestro otro triangulo rectángulo sea equivalente al primero, entonces los nuevos catetos C1 y C2 tienen que ser tal que los cocientes entre los catetos y la hipotenusa se mantengan constantes:
C1/15m = 8m/10m
C1 = (8/10)*15m = 12m
C2/15m = 6m/10m
C2 = (6/10)*15m = 9m.
Which could be used to evaluate the expression -6(2/3)
Answer: -4
Step-by-step explanation:
Do -6 x 2 to get -12, then divide by 3 to get -4
Thats assuming this is a fraction and not an actual division sign
What is the difference?
StartFraction x + 5 Over x + 2 EndFraction minus StartFraction x + 1 Over x squared + 2 x EndFraction
Answer:
[tex]\frac{x^2+4x-1}{x(x+2)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x+5}{x+2}[/tex] - [tex]\frac{x+1}{x^2+2x}[/tex] ← factor denominator
= [tex]\frac{x+5}{x+2}[/tex] - [tex]\frac{x+1}{x(x+2)}[/tex]
We require the fractions to have a common denominator.
Multiply numerator/denominator of first fraction by x
= [tex]\frac{x(x+5)}{x(x+2)}[/tex] - [tex]\frac{x+1}{x(x+2)}[/tex]
Subtract terms on numerator leaving the common denominator
= [tex]\frac{x^2+5x-x-1}{x(x+2)}[/tex]
= [tex]\frac{x^2+4x-1}{x(x+2)}[/tex]
Answer:
a on edge
Step-by-step explanation:
What is the solution to x^2-6x+9?
Answer:(x-3)(x-3)
Step-by-step explanation:
(x-3)(x-3)=x^2-6x+9
Answer:
Step-by-step explanation:
The perimeter of a right triangle is 24 meters, and the area is 24 square meters. The lengths of the sides are each multiplied by 4. What is the area of the new triangle? help
Answer:
384m
Step-by-step explanation:
24 x 4 = 96
96 x 4 = 384
Answer:
the real answer is 96
Step-by-step explanation:
How do linier equations work?
Each solution is a pair of numbers (x,y) that make the equation true. Solving a linear equation usually means finding the value of y for a given value of x. If the equation is already in the form y = mx + b, with x and y variables and m and b rational numbers, then the equation can be solved in algebraic terms.
I really hope that this helps you if u have any more questions ask. :>
Answer:
Each solution is a pair of numbers (x,y) that make the equation true. Solving a linear equation usually means finding the value of y for a given value of x. If the equation is already in the form y = mx + b, with x and y variables and m and b rational numbers, then the equation can be solved in algebraic terms.
Step-by-step explanation:
Solving an equation means finding the value or values for which the two expressions on each side of the equals sign are equal. One of the most common methods used to solve equations is the balance method.
Imagine an equation as a set of scales. The scales will stay in balance as long as the same operation (addition, subtraction, multiplication or division) is applied to both sides.
Example: y = 2x + 1 is a linear equation:
line on a graph
The graph of y = 2x+1 is a straight line
When x increases, y increases twice as fast, so we need 2x
When x is 0, y is already 1. So +1 is also needed
And so: y = 2x + 1
Here are some example values:
x y = 2x + 1
-1 y = 2 × (-1) + 1 = -1
0 y = 2 × 0 + 1 = 1
1 y = 2 × 1 + 1 = 3
2 y = 2 × 2 + 1 = 5
Topic: Probability
Only complete question 9.
Answer:
see below
Step-by-step explanation:
a. H 1, H2 ,H3 T1 ,T2, H3
b 6 possible outcomes
c 2 outcomes for the coin ( h,T) 3 outcomes for the spinner
2*3 = 6
Can someone help me with this one I’m stuck please and thank you
Answer:
none of them it should be ac,cb,ab. From my point of view
