Answer: 31.25%
Two ways to solve this problem:
#1: Use the formula: [tex]P(X=x)={n}Cx_{} *p^{x}*(1-p)^{n-x}[/tex]
#2 Use a graphing calculator and use the function binompdf(n, p, x)
x = 3n = 6p = 0.5#1: Formula:
[tex]P(X=3)=_{6}C_{3}*0.5^{3} *(1-0.5)^{6-3}=\frac{6!}{3!(6-3)!} *0.5^{3} *0.5^{3}\\=\frac{6!}{3!*3!} *0.5^{3} *0.5^{3}=20*0.125*0.125=0.3125[/tex]
#2: Faster method
binompdf(6, 0.5, 3) = 0.3125
Answer: 31.3 is the real answer.
Step-by-step explanation:
Solve for x. Round to the nearest tenth of a degree, if necessary
Answer:
31.80°
Step-by-step explanation:
In ∆ ABC :-
sin x = BC / AC sin x = 39/74 x = sin -¹ ( 39/74) x = 31.80 °10. Evaluate the function rule for the given value.
y = 12x3^for x =-2
Answer:
-96
Step-by-step explanation:
by replacing -2 on the place of x we get 12x-8= -96
Write the equation of the line (in y = ax+b form) in the
graph below. do not use any spaces when typing your
answer
Answer:
y=3x-8
Step-by-step explanation:
Jaylee bought a pair of shoes and are seems to receive some below from the store she's trying to figure out the sales tax rate that she paid for the shoes she sets up the equation one point two equals k times 28.62 and found that the sales tax rate is approximately 5.7% explain the error Jerry Lee made right the equation you could use to solve and find the correct sales tax rate
Answer:
28.62*0.057=1.63134
so about 1.63
Hope This Helps!!!
A stereo was originally priced at 75.50. it was marked down 24%. a store had a big sale of 60% off the lowest marked price. what was the final price of the stereo
Answer:
We can calculate the price with both sales by multiplying the 75.5 units of money by both percentages (to multiply them, we divide them by 100 first):
75.5 * 0.24 * 0.6 [tex]\approx.[/tex] 10.8
How to find the frequency in a histogram
Answer:Para preparar la tabla de frecuencia para un histograma, es necesario primero establecer el número de intervalos que se desea tener.
Luego, se debe determinar el ancho común de los intervalos (interval width). Para esto, se calcula la diferencia del dato mayor y el dato menor, y se divide entre el número de intervalos deseados. Este resultado se redondea al entero mayor más cercano.
Por ejemplo, si se desea tener 10 intervalos y encontramos que el dato mayor es 35 y el menor es 12,
Step-by-step explanation:
Aubrey tiene un nuevo estuche de arte con forma de prisma rectangular. El estuche es de 12 cm por 20 cm por 5cm. Lo único dentro del estuche es un nuevo borrador rosa con las dimensiones que se muestran a continuación.
¿Cual es el volumen del estuche que no ocupa por el borrador?
Respuesta:
720 cm³
Explicación paso a paso:
El volumen de un prisma rectangular viene dado por:
V = largo * ancho * alto
Dimensión de la caja de arte = 12 por 20 por 5
Dimensión del borrador = largo * ancho * alto
Volumen del borrador = 2 por 4 por 0,5
Dimensión del estuche de arte que no contiene borrador:
(12 por 20 por 5) - (2 por 4 por 0,5)
(10 por 16 por 4,5)
Volumen de la caja que no contiene borrador:
10 * 16 * 4,5 = 720 cm³
(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.
(b) Prove that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational.
Answer:
(a) [tex]x\³ - 6x - 6[/tex]
(b) Proved
Step-by-step explanation:
Given
[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root
Solving (a): The polynomial
A cubic function is represented as:
[tex]f = (a + b)^3[/tex]
Expand
[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]
Rewrite as:
[tex]f = a^3 + 3ab(a + b) + b^3[/tex]
The root is represented as:
[tex]r=a+b[/tex]
By comparison:
[tex]a = $\sqrt[3]{2}[/tex]
[tex]b = \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]
Expand
[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
Evaluate like terms
[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]
Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = 6 + 6r[/tex]
Equate to 0
[tex]f - 6 - 6r = 0[/tex]
Rewrite as:
[tex]f - 6r - 6 = 0[/tex]
Express as a cubic function
[tex]x^3 - 6x - 6 = 0[/tex]
Hence, the cubic polynomial is:
[tex]f(x) = x^3 - 6x - 6[/tex]
Solving (b): Prove that r is irrational
The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6
The divisors of -6 are: -6,-3,-2,-1,1,2,3,6
Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values
[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]
[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]
[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]
[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]
[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]
[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]
[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]
[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]
For r to be rational;
The divisors of -6 must divide f(x) without remainder
i.e. Any of the above values must equal 0
Since none equals 0, then r is irrational
The following list shows how many brothers and sisters some students have: 3, 4, 4, 5, 5, 3, 2, 4, 6, 3, 6, 4, 2 State the mode.
Answer:
mode is 4
it has the highest occurrence
Answer:
The mode is 4
Step-by-step explanation:
The mode is a value that appears most frequently in a data set.
By looking at all the numbers, the number 4 appears the most: a total of four times.
Hope it helps (●'◡'●)
Ardi and Lei are both travelling by train.
Ardi's train travels 70 km in 35 minutes.
Lei's train travels 585 km.
It leaves at 9:05 and arrives at 13:35.
Work out the difference, in km/h, between the average speed of their trains.
Answer:
10 kilometer/hour
Step-by-step explanation:
Average speed = Total distance travelled / Total time taken
Ardi:
Total distance travelled = 70 km
Total time taken = 35 minutes = 35/60 hour
Average speed = Total distance travelled / Total time taken
= 70 km ÷ 35/60 hr
= 70 × 60/35
= 4,200/35
= 120 kilometer/hour
Lei:
Total distance travelled = 585 km Total time taken = 9:05 - 13:35 = 4 hours 30 minutes
= 4.5 hours
Average speed = Total distance travelled / Total time taken
= 585 km / 4.5 hours
= 130 kilometer/hour
Difference, in km/h, between the average speed of their trains = Lei's train - Ardi's train
= 130 kilometer/hour - 120 kilometer/hour
= 10 kilometer/hour
what is the proportion 4/y= 5/10
Answer:
So, y =8
Step-by-step explanation:
4/y = 5/10
or, 4*10 = 5*y
or, 40 = 5y
or, y = 40/5
therefore, y = 8
Find the answer to each trigonometric function below.
Answer:
Sin A = [tex]\frac{opposite}{hypotenuse} =\frac{32}{40} =\frac{4(8)}{5(8)} =\frac{4}{5}[/tex]Cos C = [tex]\frac{adjacent}{hypotenuse} =\frac{16}{34}=\frac{2(8)}{2(17)} =\frac{8}{17}[/tex]Tan A = [tex]\frac{opposite}{adjacent} =\frac{21}{20}[/tex]pls help and explain answer!!
At a certain point in time, a physicist measures the
speed of a falling object to be 17.6 feet per second.
What is the equivalent speed in miles per hour?
(5280 feet = 1 mile)
Answer:
0.003 miles per hour
Step-by-step explanation:
Well since 5280 feet gives 1 mile den convert 17.6 feet per sec to miles per hr
Eva created a coffee blend for her restaurant by mixing Kenya and French Roast coffee beans. The Kenya beans cost $15 per pound and the French Roast costs $8 per pound. She bought a total of 10 pounds of coffee for a total of $97.50. Please help ASAP!!!!
Answer:
what is the question you are only telling us the fact
Step-by-step explanation:
2/5x - 1/5y = 98
2/7x - 1/14y = 55
If the ordered pair (x, y) satisfies the system of
equations shown above, what is the value of x?
Answer:
x = 140
Step-by-step explanation:
Given the equations
[tex]\frac{2}{5}[/tex] x - [tex]\frac{1}{5}[/tex] y = 98 ( multiply through by 5 to clear the fractions )
2x - y = 490 → (1)
[tex]\frac{2}{7}[/tex] x - [tex]\frac{1}{14}[/tex] y = 55 ( multiply through by 14 to clear the fractions )
4x - y = 770 → (2)
Subtract (1) from (2) term by term to eliminate y
2x + 0 = 280
2x = 280 ( divide both sides by 2 )
x = 140
Solve for X. Thank you
Answer:
x = 4
Step-by-step explanation:
The segment inside the triangle is an angle bisector and divides the opposite side into segments that are proportional to the other two sides , that is
[tex]\frac{15}{20}[/tex] = [tex]\frac{x+2}{14-(x+2)}[/tex]
[tex]\frac{3}{4}[/tex] = [tex]\frac{x+2}{14-x-2}[/tex] = [tex]\frac{x+2}{12-x}[/tex] ( cross- multiply )
4(x + 2) = 3(12 - x) ← distribute parenthesis on both sides )
4x + 8 = 36 - 3x ( add 3x to both sides )
7x + 8 = 36 ( subtract 8 from both sides )
7x = 28 ( divide both sides by 7 )
x = 4
Can someone help me with this math homework please!
Answer:
x = 12.5
Step-by-step explanation:
Explanation in progress ;-)
A farm grew 19.8 tons of wheat in 2013. The farm's wheat output increased by 9.8% from 2013 to 2014 and by 5.1% from 2014 to 2015. Which expression represents a for estimating the total output of wheat, in tons, in 2015?
A. 20 + 10 + 5
B. 20(10)(5)
C. 20 + 1.1 + 1.05
D. 20(1.1)(1.05)
Answer: Choice D
Explanation:
The increase of 9.8% rounds to 10% when rounding to the nearest ten
An increase of 10% would use the multiplier 1.1
Think of it like saying 1 + 0.10 = 100% + 10%
Similarly, the 5.1% rounds to 5% and an increase of this amount will use the multiplier 1.05
So if we started with 20 items, then 20(1.1)(1.05) is the expression that estimates an increase of 10% followed by an increase of 5%. The order doesn't matter (so you could increase by 5% first, then 10% later).
Which of the following is a composite number?
A. 1
B. 63
C.O
D. 19
B. 63
some simple googling would've been able to help you with this. but 0 isn't prime or composite, not sure about 1, 19 is prime, 63 is a definite composite
please help!!
The length of side AC is | 3,4,5,6 | units.
The area of triangle ABC is | 5,10,15,20 | square units.
Look at ∠A, the angle which resides on (1, 3). If we count 5 units down, you find the other endpoint on side AC. Hence, the length of side AC is 5 units. This figure is equal to the height of the graphed triangle.
If we mirror this process with the figure representing the triangle's length, side BC, we get 4 units.
The formula for calculating a triangle's area is [tex]\frac{1}{2}bh[/tex]. In this context, the base of the triangle is the same as the length. Now, let's plug in the base and the height.
[tex]\frac{1}{2}(4)[/tex] × [tex](5) = 10[/tex]
The area of triangle ABC is 10 squared units.
Answer:
first box: 5 second box: 10
Step-by-step explanation:
Find the product: 3/4 x 2/3. What's the product? 5/7, 6/12, 5/12, 6/7. What is it please help me!!!!
Answer:
1/2
Step-by-step explanation:
3/4 x 2/3
= 1/2
Rewrite the expression as a simplified expression containing one term.
Answer:
-(cos α)/(sin α)
= -cot α
Step-by-step explanation:
use trigonometric identities
Z Is An Even Integar Greater Than 30 And Less Than Or Equal To 34.
Answer:
32, 34
Step-by-step explanation:
The answer must be grater than 30 so 30 is not an option the integers in the range are 31, 32, 33, and 34 the only even integers in this set are 32, and 34. Hope this helps. :)
can someone help me with this please
Answer:
for question B
2A 3C = 70
70-15 = 55/5 = 11.
so each child is 11
while adult 11 + 7.50 = 18.50
what is the answer to the problem
which relation is a function?
The first one because there is only one y value for every x value. The correct option is first.
To determine if a relation is a function, use the vertical line test: If any vertical line intersects the graph of the relation at more than one point, then the relation is not a function. On the other hand, if every vertical line intersects the graph of the relation at most once, then the relation is a function.
In first relation is considered a function, because each input x-value is associated with exactly one output y-value. In other words, for every x-value in the domain of the relation, there can be only one corresponding y-value in the range. Each x-value should not have more than one y-value associated with it.
Therefore, each x-value should not have more than one y-value associated with it. The correct option is first.
Learn more about Function here:
https://brainly.com/question/31062578
#SPJ6
help I need help with my homework no link please BTW its 9th grade work I need help with number 1 a) I still need help with it
Answer:
you need to learn how to "prime factor" numbers....
primes are 2,3,5,7,11,13,17....
they go on forever. ALL whole numbers can be "broken down" into a bunch of primes multiplied together.
take the fractions (top and bottom) and start dividing them bu the smallest prime, and going up until all the numbers multiplied make the original number...
15 = 3 * 5
24= 2 * 12 = 2 * 2 * 6 = 2* 2* * 2 * 6
thus [tex]\frac{15}{24}[/tex] = [tex]\frac{3 * 5 }{2* 2* 2* 3}[/tex] now just cancel all the SAME numbers from to to bottom
"pair them up" .... in this case only one of the threes in the bottom "takes out" one of the threes in the top
result [tex]\frac{5}{2*2*2 } = \frac{5}{8}[/tex]
~~~~~~~~~~~~~~~~~~~~
[tex]\frac{21}{35}[/tex]
21= 3 * 7
35= 5* 7
[tex]\frac{3*7}{5*7} = \frac{3}{5}[/tex]
Step-by-step explanation:
You buy a 1:10000 scale model of the One World Trade Center during a trip to New York City. The height of the model is 5.41 centimeters. Find the actual height x (in meters) of the One World Trade Center.
Answer:
541m
Step-by-step explanation:
The scale given 1 represents the height of the model and 10000 represents the actual height,place the 5.41 in line with the one and an unknown letter in line with the 10000 inorder to calculate the actual height
1:10000
5.41:x
cross multiply and solve for x,which will be 54100cm
but since the answer has to be in meters convert the 54100cm to a meter by dividing it by 100..
Find the area of the triangle
Solve the equation: 12 - x (x - 3) = (6 - x)(x + 2)
Answer: the answer is 0
Why 0?:
Step 1: Simplify both sides of the equation
-x * x= -x²
-x * -3= 3x all together it is ( -x²+3x+12)
for the other side:
-x * x= -x²
6 * x= 6x and x * 2= 2x and 6 * 2= 12
then subtract 6x-4x= 2x so final would be = −x²+4x+12
Step 2: Add x² to both sides.
−x²+3x+12+x²=−x²+4x+12+x² then we are left with 3x+12=4x+12
Step 3: Subtract 4x from both sides.
3x+12−4x=4x+12−4x --> −x+12=12
Step 4: Subtract 12 from both sides.
−x+12−12=12−12
−x=0
Step 5: Divide both sides by -1 or -x
x=0
