1. A jar contains 5 red marbles numbered 1 to 5 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability that the marble is blue or odd-numbered.
We will use the following formula:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B).[/tex]First, we compute the probability that we get a blue marble:
[tex]P(\text{Blue)}=\frac{6}{5+6}=\frac{6}{11}\text{.}[/tex]Now, we compute the probability of getting an odd-numbered marble:
[tex]P(\text{odd-num)}=\frac{6}{11}\text{.}[/tex]Finally, the probability that we draw a blue and odd-numbered marble is:
[tex]P(\text{blue and odd)=}\frac{3}{11}.[/tex]Answer: The probability that the marble is blue or odd-numbered is:
[tex]\begin{gathered} P(\text{blue or odd)=P(blue)+P(odd-num)-P(blue and odd)=}\frac{6}{11}+\frac{6}{11}-\frac{3}{11}=\frac{9}{11}. \\ P(\text{blue or odd)}=\frac{9}{11}\text{.} \end{gathered}[/tex]To make an open box from a 175cm by 100cm piece of cardboard, equal-sized squares will be cut from each of the four corners and then the sides will be folded up. What is the approximate volume of the largest possible box that can be made?Group of answer choices:A) 324,146 cm^3B)162,073cm^3C) 251,707cm^3D)189,640cm^3
Given that dimensions of the piece of cardboard are:
[tex]\begin{gathered} l=175\text{ }cm \\ w=100\text{ }cm \end{gathered}[/tex]Where "l" is the length and "w" is the width, you can determine that it has the shape of a rectangle.
You know that equal-sized squares will be cut from each of the four corners and then the sides will be folded up. Then, you can make the following drawing:
By definition, the volume of a rectangle is:
[tex]Volume=length\cdot width\cdot height[/tex]In this case, you can set up that:
[tex]\begin{gathered} length=175-2x \\ width=100-2x \\ height=x \end{gathered}[/tex]Therefore, you can write this equation:
[tex]V=(175-2x)(100-2x)(x)[/tex]Expand it:
[tex]V=(175-2x)(100x-2x^2)[/tex][tex]V=(175)(100x)-(175)(2x)-(2x)(100x+(2x)(2x^2)[/tex][tex]V=4x^3-550x^2+17500x[/tex]Now you need to derivate it using the Power Derivative Rule:
[tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]Then:
[tex]V^{\prime}=(4)(3)x^2-(550)(2)x+17500[/tex][tex]V^{\prime}=12x^2-1100x+17500[/tex]Make the equation equal to zero and sove for "x":
[tex]12x^2-1100x+17500=0[/tex]Use the Quadratic Formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Substituting:
[tex]\begin{gathered} a=12 \\ b=-1100 \\ c=17500 \end{gathered}[/tex]You get:
[tex]\begin{gathered} x_1\approx20.49 \\ x_2\approx71.18 \end{gathered}[/tex]Therefore, you can make the following Sign Chart:
Then, you can substitute these:
[tex]\begin{gathered} x=20 \\ x=50 \\ x=72 \end{gathered}[/tex]Into the factorize form of the derivated function:
[tex]V=(x+\frac{275-25\sqrt{37}}{6})(x-\frac{275+25\sqrt{37}}{6})[/tex][tex]V=(x+\frac{275-25\sqrt{37}}{6})(x-\frac{275+25\sqrt{37}}{6})[/tex]Sergio believes he is five years younger than double the age of Chloe and Chloe believes she is five yearsolder than half of Sergio's age. Are they both right?
Let S represent Sergio's age
Let C represent Chloe's age
Sergio believes he is five years younger than double the age of Chloe. This would be expressed as
S = 2C - 5
Chloe believes she is five years older than half of Sergio's age. This means that
C = 5 + S/2
If we multiply the second equation by 2, it becomes
2C = 10 + S
This means that both equations are not the same. Therefore, they are not right
in health class, the students were asked what grain they prefered in their breakfast cereal. The results are shown in the table. what's the probability that a randomly chosen student in the health class listed oats as their favorite grain?A. 20%B. 25%C. 35%D. 14%
To find the probability of a randomly choosen student listing oats as its favorite grain, divide the number of students that chose oats by the total number of students and multiply the fraction by 100%.
To find the total number of students, add the numbers under each cereal:
[tex]12+14+8+6=40[/tex]The number of students who chose oats, is 14. Then, the requested probability, is:
[tex]\frac{14}{40}\times100=35\text{ \%}[/tex]You are trying to put together a chart depicting how many people by age group attended the most recent blockbuster movie What type of chart would best to use to display this Information and why-column graphs -line graphs-pie charts -bar graphs -Area charts -scatter charts
The first step will be to review all of the types of graphs or charts mentioned in the options.
The following diagram shows an example of each type of graph:
In this case, we need a graph to show the number of people by age group that attended the movie.
In this case, the line graph, the area chart, and the scatter chart will not represent the information in the best way, but a column graph, a bar graph, or a pie chart will give a better idea of the number of people by age group that went to see the movie.
Answer:
-Column graphs
-Pie charts
-Bar graphs
Can you please help me out with the a question
Arc XY = 2π • (PX)/ 4
. = 2π • 5/4
. = 6.28 • 5/4= 31.40/4 = 7.85
Then answer is
Option G) 7.854
Refer to the rectangle ABCD, shown below, where m(<4)=10degrees. Need help.
From the statement of the problem, we know that:
[tex]m(\angle4)=18^{\circ}\text{.}[/tex]From the diagram, we see that:
1) ∠1 and ∠4 are complementary angles, so they sum up 90°:
[tex]\begin{gathered} m\mleft(\angle1\mright)+m\mleft(\angle4\mright)=90\degree \\ m\mleft(\angle1\mright)=90\degree-m\mleft(\angle4\mright), \\ m(\angle1)=90\degree-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]2) ∠4, ∠3 and a right angle are inner angles of a triangle, so they must sump up 180°:
[tex]\begin{gathered} m(\angle4)+m(\angle3)+90^{\circ}=180^{\circ}\text{.} \\ m(\angle3)=180^{\circ}-90^{\circ}-m(\angle4), \\ m(\angle3)=180^{\circ}-90^{\circ}-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]3) ∠3 and ∠2 are complementary angles, so they sum up 90°:
[tex]\begin{gathered} m(\angle3)+m(\angle2)=90^{\circ}, \\ m(\angle2)=90^{\circ}-m(\angle3), \\ m(\angle2)=90^{\circ}-72^{\circ}=18^{\circ}\text{.} \end{gathered}[/tex]Answer
c. m(∠1) = 72°, m(∠2) = 18°, m(∠3) = 72°.
The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m^s. Find the dimensions.
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Write the formula for total surface area of cuboid
[tex]\begin{gathered} 2(lb+bh+lh) \\ \text{where l is the length} \\ b\text{ is the breadth} \\ \text{h is the height} \end{gathered}[/tex]STEP 2: Get the dimension of the sides
[tex]\begin{gathered} \text{ Since the dimensions of the cuboid are in the ratio 1:2:3} \\ the\text{ dimensions are given as:} \\ x,2x\text{ and }3x \\ \text{lenght}=x \\ \text{breadth}=2x \\ \text{height}=3x \end{gathered}[/tex]STEP 3: Substitute the dimensions into the formula to get the value of x
[tex]\begin{gathered} 2(lb+bh+lh)=88 \\ By\text{ substitution,} \\ 2((x\cdot2x)+(2x\cdot3x)+(x\cdot3x))=88 \\ \Rightarrow2(2x^2+6x^2+3x^2)=88 \\ \text{Divide both sides by 2} \\ \Rightarrow\frac{2(2x^2+6x^2+3x^2)}{2}=\frac{88}{2} \\ \Rightarrow2x^2+6x^2+3x^2=44 \\ 11x^2=44 \\ \text{Divide both sides by 11} \\ \frac{11x^2}{11}=\frac{44}{11} \\ x^2=4 \\ x=\sqrt[]{4}=2 \\ x=2m \end{gathered}[/tex]STEP 4: Get the other dimensions
[tex]\begin{gathered} \text{breadth}=2x \\ \text{substitute 2 for x} \\ \text{breadth}=2(2)m=4m \\ \\ To\text{ get height} \\ \text{height}=3x \\ \text{substitute 2 for x} \\ \text{height}=3(2)m=6m \end{gathered}[/tex]Hence, the dimensions are:
[tex]2m,4m,6m[/tex]Determine if u is a solution to 1 - 9u = 19u= -2, 7, 0, 6
-2
Replace u by -2, and check if the equality remains
1-9u = 19
1-9(-2) = 19
1-(-18)=19
1+18 = 19
19=19
-2 YES
7
1- 9(7) = 19
1-63 = 19
-62=19
NO
0
1-9(0) = 19
1= 19
NO
6
1-9(6) = 19
1-54=19
-53=19
NO
In one year, the CPI increased from 106.3 to 108.9. How much money was required at the end of the year in order to have the same purchasing power as $1,000 at the beginning?
Based on the increase in CPI, the amount that would be required at year end to have the same purchasing power at the beginning of the year is $1,024.46.
How to find the change in purchasing power?First, find the inflation rate:
= (Current CPI - Beginning CPI) / Beginning CPI
= (108.9 - 106.3) / 106.3
= 2.446%
This means that the amount of money at the beginning of the year has lost a value of 2.446%.
In order to remain the same as the value of $1,000, a person would need:
= 1,000 x (1 + 2.446%)
= $1,024.46
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A polynomial function is given.
Q(x) = −x2(x2 − 9)
(a) Describe the end behavior of the polynomial function.
End behavior: y → as x → ∞
y → as x → −∞
The end behavior of the polynomial is:
y → −∞ as x → ∞
y → −∞ as x → −∞
How is the end behavior?Here we have the polynomial:
Q(x) = -x²*(x² - 9)
Remember that polynomials with even degrees have the same behavior for the negative values of x than for the positive, in this case if we expand the polynomial we get:
Q(x) = -x⁴ + 9x²
The leading coefficient is negative, then the end behavior will tend to negative infinity in both ends, then we get:
y → −∞ as x → ∞
y → −∞ as x → −∞
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The illustration below shows the graph of y as a function of x.complete the following sentences based on the graph of the function.* initially, as x increases, y (increases, decreases or stays constant).* the slope of the graph is equal to ___ for all x between x = 0 and x = 3.* starting at x = 3, the function value y (increases, decreases, or stays constant) as x increases.* the slope of the graph is equal to ___ for x between x = 3 and x = 5.* for x between x = 0 and x = 4, the function value y (≤, ≥, or =) 0.* for x between x = 4 and x = 8, the function value y (≤, ≥, or =) 0.
We will have the following:
*Initially, as x increases, y decreases.
*The slope of the graph is equal to -1 for all x between x = 0 & x = 3.
*Starting at x = 3, the function value y increases as x increases.
*The slope of the graph is equal to 3 for x between x = 3 & x = 5.
*For x between x = 0 & x = 4, the function value y ≤ 0.
*For x between x = 4 & x = 8, the function value y ≥ 0.
After reading the question what would the inequality equation and the graph shade look like?
It is given that the one number is always less than the opposite of the other.
So the equation formed is y<-x
The graph is obtained as
Question 16
Given AEFHAGFH below, what is the measure of GFH?
F
21.6°
E<
(6x - 12)° H
G
1 pts
The most appropriate choice for congruency of triangles will be given by-
[tex]\angle GFH =68.4^{\circ}\\[/tex]
What is congruency of triangles?
Two triangles are said to be congruent if all the corrosponding sides and the corrosponding angles of the triangle are equal.
There are five axioms of congruency. They are -
SSS axioms, SAS axioms, ASA axiom, AAS axiom, RHS axiom.
Here,
[tex]\Delta EFH \cong \Delta GFH[/tex] [Given]
[tex]\angle E = \angle G = 21.6^{\circ}[/tex] [Corrosponding parts of congruent triangles are congruent]
[tex]\angle GFH[/tex] = 180 - (90 + 21.6) [Sum of the three angles of a triangle is 180°]
[tex]\angle GFH = 180 - 111.6\\\angle GFH =68.4^{\circ}\\[/tex]
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A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 17.6 ft. give the area A of the window in square feet when the width is 4.1 ft. Give the answer to two decimals places.
To find the area of the window you need to find the area of rectangular part and the area of semicircle part.
To find the area of the rectangular part you need to find the height of the rectangle, use the perimeter to find it:
Perimeter of the given window is equal to: The circunference or perimeter of the semicircle (πr) and the perimeter of the rectangular part (w+2h)
[tex]P=\pi\cdot r+w+2h[/tex]The radius of the semicircle is equal to the half of the width:
[tex]\begin{gathered} r=\frac{4.1ft}{2}=2.05ft \\ \\ w=4.1ft \\ \\ P=17.6ft \\ \\ 17.6ft=\pi\cdot2.05ft+4.1ft+2h \end{gathered}[/tex]Use the equation above and find the value of h:
[tex]\begin{gathered} 17.6ft-\pi\cdot2.05ft-4.1ft=2h \\ 7.06ft=2h \\ \\ \frac{7.06ft}{2}=h \\ \\ 3.53ft=h \end{gathered}[/tex]Find the area of the rectangular part:
[tex]\begin{gathered} A_1=h\cdot w \\ A_1=3.53ft\cdot4.1ft \\ A_1=14.473ft^2 \end{gathered}[/tex]Find the area of the semicircle:
[tex]\begin{gathered} A_2=\frac{\pi\cdot r^2}{2} \\ \\ A_2=\frac{\pi\cdot(2.05ft)^2}{2} \\ \\ A_2=6.601ft^2 \end{gathered}[/tex]Sum the areas to get the area of the window:
[tex]\begin{gathered} A=A_1+A_2 \\ A=14.473ft^2+6.601ft^2 \\ A=21.074ft^2 \end{gathered}[/tex]Then the area of the window is 21.07 squared feetabout 23% of people are at a higher risk of stroke due to other medical conditions like high blood pressure. their risk is about 9% of stroke compared with the general population's 3% chance of having a stroke in their lifetime.
Make the following conversions.5 pounds 16 ounces toa. Ounces:? ozb. Pounds: ? lbNote : I have attempted 80 ounces in 1 pound as the answers and it is incorrect
In order to calculate these conversions, we need to know the following conversion rate:
1 pound is equal to 16 ounces.
Knowing that, let's convert:
a. to ounces:
[tex]5\text{ pounds 16 ounces }=5\cdot16\text{ ounces + 16 ounces}=80\text{ + 16 ounces }=96\text{ ounces}[/tex]b. to pounds:
[tex]5\text{ pounds 16 ounces }=5\text{ pounds + 1 pound }=6\text{ pounds}[/tex]Determine (Freshman) Small Cafeteria). Interpret this answer in the context of the situation.
Step 1:
[tex]\text{Probability = }\frac{N\text{umber of required outcomes}}{N\text{umber of total possible outcome}}[/tex]Step 2:
a)
Total possible outcome = 2640
Total number of freshman = 625
[tex]\begin{gathered} P(\text{Freshman) = }\frac{625}{2640} \\ \text{= }\frac{125}{528} \\ \text{= 0.237} \end{gathered}[/tex]Step 3:
b)
Total number of senior and large cafeteria = 350
[tex]\begin{gathered} P(\text{senior and large cafeteria) = }\frac{350}{2640} \\ =\text{ }\frac{70}{528} \\ =\text{ }\frac{35}{264} \\ =\text{ 0.132} \end{gathered}[/tex]Step 4:
c)
Number of Sophomore or student center = 650 + 595 - 125 = 1120
[tex]\begin{gathered} P(\text{Sophomore or student center) = }\frac{1120}{2640} \\ =\text{ }\frac{112}{264} \\ =\text{ 0}.424 \end{gathered}[/tex]Step 5:
d)
[tex]\begin{gathered} p(\text{freshman}|\text{small cafeteria) = }\frac{n(freahman\text{ and small cafeteria)}}{n(small\text{cafeteria)}} \\ =\frac{435}{860}\text{ } \\ =\text{ }\frac{87}{172} \\ =\text{ 0.506} \end{gathered}[/tex]22. This question has two parts.Aya sold printed T-shirts for $7.50 each at a carnival. She earned$187.50.Part A. Which equation represents the number of T-shirts, x, Aya sold atthe carnival?7.50x = 187.50187.50x = 7.50x + 7.50 = 187.50x - 7.50 = 187.50Part B. What is the number of T-shirts Aya sold at the carnival?0.04B25180195
Explanation
Step 1
Aya sold printed T-shirts for $7.50 each at a carnival. She earned
$187.50.
then
let x represents the number of T-shirts Aya sold.so, if she made $187.5 and the cost per T-shirt is $7.50
[tex]\begin{gathered} \text{total}=\text{ rate}\cdot\nu mber\text{ of T-shirt} \\ \text{replace} \\ 187.5=7.5x \\ or \\ 7.50x=187.50 \end{gathered}[/tex]therefore, for part A , the answer is
[tex]A)7.50x=187.5[/tex]
Step 2
What is the number of T-shirts Aya sold at the carnival?
to figure out this,we need to solve for x
[tex]\begin{gathered} 7.5x=187.5 \\ \text{divide both sides by 7.5} \\ \frac{7.5x}{7.5}=\frac{187.5}{7.5} \\ x=25 \end{gathered}[/tex]it means she sold 25 T-shirts at the carnival
I hope this helps you
Question 2 Multiple Choice Worth 2 points)(08.07 LC)Two friends are reading books. Jimmy reads a book with 21,356 words. His friend Bob reads a book with one-and-a-half times as many words. Which expressionrepresents the number of words Bob reads?O 21,356 x 2O 21,356 x6 x 1nents1adesO 21,356 xO 21.356 x112Question 3 Multiple Choice Worth 2 points)(08.07 LC)Question 1 (Answered)OVIOUS QuestionNexd Quest
The number of words of the book Jimmy reads os 21,356, and the number of words of the book Bob reads is one-and-a-half times (that is, 1.5x) as many words, so to find the number of words Bob reads, we just need to multiply the number of words of Jimmy's book by the factor of 1.5:
[tex]21356\cdot1.5=32034[/tex]10x + 45x - 13 = 11(5x + 6)
We have to find the solution for the equation:
[tex]\begin{gathered} 10x+45x-13=11\cdot(5x+6) \\ 55x-13=11\cdot5x+11\cdot6 \\ 55x-13=55x+66 \\ 55x-55x=66+13 \\ 0\cdot x=79 \end{gathered}[/tex]The equation has no solution, becuase there is no value of x that satisfy the equation.
rst builds ons 3 Veronda has a bag of mixed shapes. She chooses 3 shapes and fits them together to form a figure as shown. 17 cm What is the area of the figure Veronda creates? Use 1 = 3.14 5 Holly A 136 cm? B 107.14 cm C 96.56 cm D 76.57 cm?
We have three different figures
Semicircle
r = 4cm
[tex]\begin{gathered} A_r=\frac{\pi\cdot r^2}{4} \\ A_r=\frac{3.14\cdot4^2}{4} \\ A_r=\frac{3.14\cdot16}{4} \\ A_r=12.56 \end{gathered}[/tex]Square
l = 8cm+
Endpoint: (1,3) Midpoint: (-2,5) Please I need help ASAP
Graph the function f(x) = 4 sin(-2x) on the graph below
Answer:
Explanation:
Here, we want to plot the graph of f(x)
The general equation of a sine graph is:
[tex]y\text{ = A sin (Bx + C) + D}[/tex]where A is the amplitude of the curve
B is -2
C is 0
D is 0
Mathematically, the period of the graph and B are related as follows:
[tex]\begin{gathered} \text{Period = }\frac{2\pi}{|B|} \\ \\ Period\text{ = }\frac{2\pi}{2} \\ \\ \text{Period = }\pi \end{gathered}[/tex]What this means is that the distance between two peaks on the graph is pi
We have the plot as follows:
Can anyone help with a step by step solution asap thank you
The value of the expression x² + 5x + 4 is found as 4.
What is termed as the quadratic expression?A quadratic expression is one that has the variable with highest power of two. A quadratic expression is one that has the form ax² + bx + c, in which a ≠ 0.Typically, the expression is written in the form of x, y, z, or w.In such a quadratic expression brought up to the power of 2, the variable 'a' cannot be zero. If a = 0, x² is multiplied by zero, and the expression is no longer a quadratic expression.Variables b and c with in standard form can indeed be zero, but variable a cannot.for the given question,
The quadratic expression is given as;
= x² + 5x + 4
Put x = -5
= (-5)² + 5(-5) + 4
Simplifying.
= 25 - 25 + 4
25 will get cancelled.
= 4
Thus, the value of the expression is found as 4.
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I attached the questions as images. The first image is actually the second.You can send in the work on paper like the graphing part.The questions can be typed on the solution tab or messages whichever is easier for you.Thanks again for the help :)
SOLUTION
Consider the image below,
The lenght of the compass is the radius, using a lenght of 5 unit, we have circle below as the sphere .
Where
[tex]\begin{gathered} r=\text{ radius, O= origin } \\ And \\ r=5\text{unit } \end{gathered}[/tex]Using the formula, we have
[tex]\begin{gathered} \text{Volume of sphere} \\ =\frac{4}{3}\pi r^3 \\ \text{where} \\ \pi=3.14,\text{ r=}5 \end{gathered}[/tex]Substitute into the formula, we have
[tex]\begin{gathered} \text{Volume of the sphere is } \\ =\frac{4}{3}\times3.14\times5^3 \\ \text{Hence } \\ 523.33\text{ cubic unit} \end{gathered}[/tex]Therefore
The volume of the sphere is 523.33 cubic unit
if (x + y) +61 = 2, what is x + y?
The question is given as
[tex](x+yi)+6i=2[/tex]To solve, we need to make (x + yi) the subject of the formula.
To do so, we move 6i to the right-hand side of the equation:
[tex]x+yi=2-6i[/tex]Therefore, OPTION A is correct.
Answer:
(x + yi)= 2-6i
Step-by-step explanation:
Complex numbers
(x + yi) +6i = 2
Subtract 6i from each side
(x + yi) +6i -6i = 2-6i
(x + yi)= 2-6i
it says find x 110° x and 25° in a triangle
There are two known angles in such a manner:
We know that the sum of internal angles of a triangle is equal to 180 degrees. This means that we can find the missing angle by adding all the internal angles and making it equal to 180
[tex]\begin{gathered} 25+110+x=180 \\ 135+x=180 \\ x=180-135 \\ x=45 \end{gathered}[/tex]The missing angle is 45 degrees.
I need to the equation of a line as (-5,-3); slope = -3/5
To answer this question, we will use the following formula for the equation of a line that passes through (x₁,y₁), and has slope m:
[tex]y-y_1=m(x-x_1)\text{.}[/tex]Substituting (x₁,y₁)=(-5,-3) and m=-3/5 in the above formula we get:
[tex]y-(-3)=-\frac{3}{5}(x-(-5))\text{.}[/tex]Simplifying the above equation we get:
[tex]\begin{gathered} y+3=-\frac{3}{5}(x+5), \\ y+3=-\frac{3}{5}x-\frac{3}{5}5, \\ y+3=-\frac{3}{5}x-3, \\ y+3-3=-\frac{3}{5}x-3-3, \\ y=-\frac{3}{5}x-6. \end{gathered}[/tex]Answer:
[tex]y=-\frac{3}{5}x-6\text{.}[/tex]the difference between 58% of a number and 39% of the same number is 247. what is 62% of that number
Answer
62% of the number = 806
Explanation
We are told that that the difference between 58% of a number and 39% of the same number is 247.
We are then asked to compute 62% of the number.
Let the number be x.
From the first statement,
58% of x = 0.58 × x = 0.58x
39% of x = 0.39 × x = 0.39x
The difference between them is 247
0.58x - 0.39x = 247
0.19x = 247
Divide both sides by 0.19
(0.19x/0.19) = (247/0.19)
x = 1300
So, we can now calculate 62% of the number
62% of x = 0.62 × x = 0.62 × 1300 = 806
Hope this Helps!!!
