Answer:
Dominic ate [tex]\frac{2}{6}[/tex] of the pizza.
Step-by-step explanation:
First you want to convert the fractions so they all have the same denominator (bottom number in the fraction.) That will make it a lot easier to add and subtract with them.
[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{6}[/tex]
So Shawn ate 1/6 of the pizza, and Ryan ate 3/6 of the pizza. To find what else makes up the whole pizza (what Dominic ate) we add 1/6 and 3/6, then subtract from the whole.
[tex]\frac{1}{6}[/tex] + [tex]\frac{3}{6}[/tex] = [tex]\frac{4}{6}[/tex]
[tex]\frac{6}{6}[/tex] - [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{6}[/tex]
Therefore Dominic ate [tex]\frac{2}{6}[/tex] of the pizza.
3. Two dice are rolled. What’s the conditional probability that both dice are 5’s if it’s known that the sum of points is divisible by 5?
Answer:
[tex]Pr =\frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]S = \{(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]
[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]
[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)\}[/tex] --- sample space
First, list out all outcomes whose sum is divisible by 5
[tex]A = \{(4,6), (5,5),(6,4)\}[/tex]
So, we have:
[tex]n(A) = 3[/tex]
Next, list out all outcomes that has an outcome of 5 in both rolls
[tex]B = \{(5,5)\}[/tex]
[tex]n(B) =1[/tex]
The required conditional probability is:
[tex]Pr =\frac{n(B)}{n(A)}[/tex]
[tex]Pr =\frac{1}{3}[/tex]
what is the answer to this? i can’t figure it out.
9514 1404 393
Answer:
25 +0i
Step-by-step explanation:
The conjugate of a complex number is that number with the sign of the imaginary part reversed.
For z = -3+4i, its conjugate z* is -3-4i. The product of z and z* is ...
(-3 +4i)(-3 -4i) = -3(-3 -4i) +4i(-3 -4i)
= 9 +12i -12i -16i² = 9 +16 = 25
The real part of the product is 25; the imaginary part is 0.
(-3 +4i)(-3 -4i) = 25 +0i
_____
You may have noticed that (z)(z*) = |z|², the sum of the squares of the real and imaginary parts. It is always a non-negative real number.
Can someone help me with this question please..
Answer:
The ordered pair would be (2,3)
2 in the first Box
3 in the second
solve for this square.
Answer:
a2
b4
c16 brainliest plzz
Answer:
a) SV = 2
The line that is SV actually is not the full slash. It is halfway, and we know that half of four would be two.
b) RT = 4
This time RT is a full line going all the way down. So it would be 4.
c) p = a + b + c
The lengths are all the same because we calculated in the first question that two is half of four. So the base, height, and hypotenuse are the same, 2.
2 + 2 + 2 = 6
So the perimeter of the triangle RVS is 6.
A manufacturer knows that their items have a lengths that are skewed right, with a mean of 10 inches, and standard deviation of 1.6 inches. If 39 items are chosen at random, what is the probability that their mean length is greater than 10.5 inches
Solution :
Given :
Mean, μ = 10 inches
Standard deviation, σ = 1.6 inches
Sample size is n = 39
Therefore,
[tex]$\mu_{\overline x}=\mu = 10$[/tex]
[tex]$\sigma_{\overline x}=\frac{\sigma}{\sqrt n } = \frac{1.6}{\sqrt{39}}$[/tex]
= 0.25
[tex]$P (\overline X > 10.5 ) = P\left( \frac{\overline X - \mu_{\overline x}}{\sigma_{\overline x}} > \frac{10.5 - 10}{0.25} \right)$[/tex]
= P( Z >2)
= 1 - P(Z < 2)
= 1 - 0.97225 (from standard normal table)
= 0.0277
please help me find the area
Answer:
320 square feet.
Step-by-step explanation:
For the moment, let's put the square back in place. That would make the length 16 + 8 = 24 and the width 16.
L = 24
W = 16
Area = L * W
Area = 24 * 16
Area = 384
Now the next step is to take out the square. It is 8 * 8 = 64
The area of the figure = 384 - 64 = 320 square feet, and that's the answer.
Answer:
320 in^2
Step-by-step explanation:
we need to find the area of this figure
Firstly divide above picture in two parts
1st figure = (16*16)in.
2nd figure = (8*8)in.
Area of 1st figure = 16*16 = 256 in^2
Area of 2nd figure = 8*8 = 64 in^2
Area of whole figure = ( 256 + 64 )in^2
= 320 in^2
Consider the following hypothesis test. : : The following results are for two independent samples taken from two populations. Excel File: data10-03.xlsx Enter negative values as negative numbers. a. What is the value of the test statistic? (to 2 decimals) b. What is the -value? (to 4 decimals) c. With , what is your hypothesis testing conclusion? - Select your answer -
Answer:
[tex]z = -1.53[/tex] --- test statistic
[tex]p = 0.1260[/tex] --- p value
Conclusion: Fail to reject the null hypothesis.
Step-by-step explanation:
Given
[tex]n_1 = 80[/tex] [tex]\bar x_1= 104[/tex] [tex]\sigma_1 = 8.4[/tex]
[tex]n_2 = 70[/tex] [tex]\bar x_2 = 106[/tex] [tex]\sigma_2 = 7.6[/tex]
[tex]H_o: \mu_1 - \mu_2 = 0[/tex] --- Null hypothesis
[tex]H_a: \mu_1 - \mu_2 \ne 0[/tex] ---- Alternate hypothesis
[tex]\alpha = 0.05[/tex]
Solving (a): The test statistic
This is calculated as:
[tex]z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} }}[/tex]
So, we have:
[tex]z = \frac{104 - 106}{\sqrt{\frac{8.4^2}{80} + \frac{7.6^2}{70} }}[/tex]
[tex]z = \frac{104 - 106}{\sqrt{\frac{70.56}{80} + \frac{57.76}{70}}}[/tex]
[tex]z = \frac{-2}{\sqrt{0.8820 + 0.8251}}[/tex]
[tex]z = \frac{-2}{\sqrt{1.7071}}[/tex]
[tex]z = \frac{-2}{1.3066}[/tex]
[tex]z = -1.53[/tex]
Solving (b): The p value
This is calculated as:
[tex]p = 2 * P(Z < z)[/tex]
So, we have:
[tex]p = 2 * P(Z < -1.53)[/tex]
Look up the z probability in the z score table. So, the expression becomes
[tex]p = 2 * 0.0630[/tex]
[tex]p = 0.1260[/tex]
Solving (c): With [tex]\alpha = 0.05[/tex], what is the conclusion based on the p value
We have:
[tex]\alpha = 0.05[/tex]
In (b), we have:
[tex]p = 0.1260[/tex]
By comparison:
[tex]p > \alpha[/tex]
i.e.
[tex]0.1260 > 0.05[/tex]
So, we fail to reject the null hypothesis.
i need help finding m<1 please :)
Answer
c,116°
Step-by-step explanation:
i don't know how to draw a diagram?
Join ends of chord with the center making angles ∠2,∠3 and angle at the center.
angle at the center=128°
∠1=∠2+90°
∠2=∠3
∠2+∠3+128=180
∠2+∠2+128=180
2∠2=180-128=52
∠2=52/2=26
∠1=26+90=116°
sorry i can't explain properly without picure.
f(x) = 3x + 10
х
f(x)
-3
-2
-1
-4
Pythagorean triples are super important to know. If the hypotenuse of a triangle is 15, what are its legs ( hint - use the three, four, five triple)
Answer:
9, 12
Step-by-step explanation:
Just multiply the 3,4,5 triple by 3 and u get 9, 12, 15
Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5 (and your wager) for rolling a 5 or a 2, nothing otherwise. What are your expected net winnings, to the nearest cent?
Solve the following system. If the system's equations are dependent or if there is no solution, state this.
12a+35b= 19
24a+8c= 1
28b+8c= 5
A) There is one solution. The solution is (__,__,__)
B) The system is dependent
C) There is no solution
Answer:
the answer is c .no solution
I need help please anyone
Answer:
base: 3units
height: 5units
Area:15units square
Step-by-step explanation:
you can count the squares in the figure to know the base and hight.
Area of parallelogram= base x height= 3x5= 15 units square.
please give me brainliest, thanks!
A chemist is using 331 milliliters of a solution of acid and water. If 16.2% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
9514 1404 393
Answer:
53.6 mL
Step-by-step explanation:
The amount of acid is 16.2% of 331 mL, or ...
0.162 × 331 mL = 53.622 mL
There are about 53.6 mL of acid in the solution.
if sec theta = - √30 / 3, find cos theta.
if sin(-theta) = -0.97, find cos (π/2 - theta).
Step-by-step explanation:
[tex] \cos \theta = \frac{1}{ \sec\theta } = - \frac{3}{ \sqrt{30} } = - \frac{3 \sqrt{30} }{30} = - \frac{ \sqrt{30} }{10} [/tex]
[tex] \cos( \frac{\pi}{2} - \theta )= \cos \frac{\pi}{2} \cos \theta + \sin \frac{\pi}{2} \sin \theta [/tex]
Note that
[tex] \sin( - \theta) = - \sin \theta[/tex]
[tex] \cos \frac{\pi}{2} = 0 \: \: \: \: \: \sin \frac{\pi}{2} = 1[/tex]
Therefore,
[tex] \cos( \frac{\pi}{2} - \theta ) = 0.97[/tex]
6(x + 2) in the simplest form
Using the Distributive Property we can put this in its simplest form.
6(x+2)
(6)(x)+(6)(2)
6x+12
Answer:
6x + 12
Step-by-step explanation:
Use the distributive property to multiply the 6 to the x and 2 to get 6x + 12.
Your cell phone plan costs 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan.
Answer: Umm lemme try this
Step-by-step explanation:
55+35=x
Which equation represents a circle with a center at (–3, –5) and a radius of 6 units?
Answer:
Step-by-step explanation:
The general equation of the circle is:
(x-h)²+(y-k)²=r²
(h, k)=(-3,-5) are the coordinates of the center of the circle.
r=6 is the radius
The equation of the circle is:
(x+3)²+(y+5)² = 36
I need help ASAP please anyone
Answer:
112
Step-by-step explanation:
Answer:
112
Step-by-step explanation:
4×4= 16×2=32
5×4= 20×2=40
5×4= 20×2=40
Total = 112
I need to know the answer this is confusing
Answer:
46
Step-by-step explanation:
102 + 32 = 134
180 - 134 = 46
x = 46
for the function x^2+8x+7
evaluate f(4)
Answer:
I think you would have to plug in 4 as X so it would be 4^2 +8(4)+ 7
that would be 16+ 32 +7 and that would equal 55
what is not an angle pair?
Answer:
A pair of angles whose sum is not 90 or 180 is not an angle pair.
look at pic 10 pts will mark brainilest
Answer:
Step-by-step explanation:
[tex]9\frac{1}{8} = 2\frac{1}{4} +x[/tex]
[tex]\frac{9*8+1}{8} =\frac{4*2+1}{4} +x[/tex]
[tex]\frac{73}{8} =\frac{9}{4} +x[/tex]
[tex]\frac{73}{8} =\frac{9+4*x}{4}[/tex]
do cross multiplication
[tex]8(4x+9)=4*73\\32x+72=292\\32x=292-72\\x=220/32\\x=6.875[/tex]
When g(x) = 3x, what is g(5)?
Answer:
g(5) = 15
Explanation:
If the x in g(x) is 5 then the x beside 3 would also be 5.
g(5) = 3(5)
g(5) = 15
Hope this helps, good luck!
Answer:
g(5)= 15
Step-by-step explanation:
g(x) = 3x and in this situation x =5 ( g(5) )
so substitute x for 5 in the original equation:
g(x) = 3x --> g(5) = 3(5)
which gives you 15. Hope this helps!
Alex wants to arrange chairs in such a way that the number of chairs in a row is equal to the number of columns. He has ordered 5100 tables.
a)How many more tables needed to arrange in such a way that he planned? Justify your answer
2)How many chairs can he remove to arrange in a way that he wants? Justify your answer.
Answer:
84
59
Step-by-step explanation:
In other to have the same number of chayes in both rows and columns ;
If the Number of chairs per row = x ; then number of chairs per column = x
Then the total number of chairs needed = x * x = x²
Hence, if there are 5100 chairs ;
Number of chairs needed more ;
Take the square root of 5100 ;the round to the next whole number :
B.) For number of chairs to be removed ;
Take the square root of 5100 and round down to the whole number.
Hence,
A.) = √5100 = 71.414 = 72
72² - 5100 = 84
B.) 5100 = 71.414 = 71
5100 - 71² =
2(x+3)=x-4
please help me <3
2. The cost of oranges varies directly with the total mass bought. 2 kg of oranges costs $4.50. Describe the relationship between cost and mass in words. You may want to calculate a unit rate first.
Answer:
The relationship between the cost/mass is $2.25/kg.
Step-by-step explanation:
You first need to divide $4.50 / 2, to know what a single kilogram mass costs.
$4.50 / 2 = $2.25
Now that you have this unit rate $2.25, You can multiply/add it.
$4.50 + $2.25 is $6.75, + another $2.25 = $9.00, and so on.
What is the solution set for the quadratic inequality x2 – 5 ≤ 0?
Answer: -4...?
Step-by-step explanation:
Kayla wants to fence in a rectangular dog pen that is 30 ft by 40 ft How would you use wha
you know about geometry to help her ensure that she has truly built a rectangular pen?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the dimension of the dog pen = 30 ft by 40 ft.
Using the knowledge of geometry, that know that a rectangle has been built, the area of the pen should be :
Area of rectangle = Length * width
Area = 40 * 30
Area = 1200 ft²
Perimeter of rectangle = 2(Length + width)
Perimeter = 2(40 + 30)
Perimeter = 2(70)
Perimeter = 140 feets
Hence, area of the pen should be 1200 ft² and its perimeter or fencing should measure 140 feets
At Misu's Ice Cream Parlor, their famous 4-layer ice cream cake consists of four layers of ice
cream alternating with layers of cake. If there are 8 flavors of ice cream, and we count
different cakes based on the order of ice cream layers from top to bottom:
a) how many different cakes can be made if flavors can be repeated?
Answer:
4096 different cakes can be made if flavors can be repeated.
Step-by-step explanation:
Since at Misu's Ice Cream Parlor, their famous 4-layer ice cream cake consists of four layers of ice cream alternating with layers of cake, if there are 8 flavors of ice cream, and we count different cakes based on the order of ice cream Layers from top to bottom, to determine how many different cakes can be made if flavors can be repeated, the following calculation must be performed:
8 x 8 x 8 x 8 = X
64 x 64 = X
4.096 = X
Therefore, 4096 different cakes can be made if flavors can be repeated.
