Given,
The number of cards in a standard deck is 52.
Required:
The probability of drawing of spade card.
The number of spade card in deck is 13.
Consider,
A is the event of drawing of spade card.
Probability is calculated as:
[tex]Probability\text{ =}\frac{Number\text{ of favourable events}}{Total\text{ events}}[/tex]Substituting the values then,
[tex]\begin{gathered} P(A)\text{=}\frac{N(A)}{Total\text{ events}} \\ =\frac{13}{52} \\ =\frac{1}{4} \end{gathered}[/tex]Hence, the probability is 1/4.
I need help find the answer to number 10 and 11
10. We need to identify the value of b in the function:
[tex]f(x)=b^x[/tex]so that it produces the graph given.
Observing the graph, we see that the point (1,2) lies on it. Thus, we have:
[tex]\begin{gathered} 2=b^1 \\ \\ \Rightarrow2=b \end{gathered}[/tex]Therefore, the value of the base b is: 2
Sowen rolled two number cubes with sides numbered 1 through 6, 20 times. Her sums are recorded in the table below.49899462.1012879111087935What is the experimental probability of rolling a sum of 9?4/20Сь5/20Od4/365/36
The total number of experiment, N=20.
From the given data, 9 is obtained 5 times.
The number of times of getting 9, n=5.
Hence, the probability of getting a sum of 9 is,
[tex]\begin{gathered} P=\frac{n}{N} \\ P=\frac{5}{20} \end{gathered}[/tex]Hence, option b is correct.
902 degrees Celsius round the temperature to the nearest ten
The temperature is 92 degrees celsius. Rounding 92 degrees celsius to the nearest ten will be 90 degrees celsius. The closest ten to 92 is definitely 90.
Therefore,
[tex]92^{\circ}\approx90^{\circ}(To\text{ the nearest tens)}[/tex]Convert percent to fraction and simplify if possible 11% =
To convert percent to fraction divide it by 100
Then to change 11% to a fraction divide 11 by 100
[tex]\frac{11}{100}[/tex]Since 11 and 100 can not divide by the same number, then
11% = 11/100 in the simplest form
use the formula for computing future value using compound interest to determine the value of an account at the end of 10 years if a principal amount of $10,000 is deposited in an account at an annual rate of 3% and the interest is compounded quarterly. The amount after ten years will be $_______ (round to the nearest cent as needed). A = P ( 1 + r/m) ^ n
Given:
P=$10000 : m=4 : r=0.03 : n=40
[tex]A=P(1+\frac{r}{m})^n[/tex][tex]A=10000(1+\frac{0.03}{4})^{40}[/tex][tex]A=10000(1.0075)^{40}[/tex][tex]A=10000(1.3483)[/tex][tex]A=\text{ \$13483}[/tex][tex]1\text{ \$= 100 cent}[/tex][tex]A=13483\times100[/tex][tex]A=\text{ 1348300 cent}[/tex]Therefore,The amount after ten years will be 1348300 cent.
how do I solve (-2+5i) (4-i) +(2-i)
Given:
[tex](-2+5i)(4-i)+(2-i)[/tex]Using the distributive property for the multiplication then combine the like terms
so, the given expression will be:
Note: i² = -1
[tex]\begin{gathered} (-2+5i)(4-i)+(2-i) \\ =-2(4-i)+5i(4-i)+(2-i) \\ =-8+2i+20i-5i^2+2-i \\ =-8+2i+20i+5+2-i \\ =(-8+5+2)+(2i+20i-i) \\ =-1+21i \end{gathered}[/tex]So, the answer will be:
[tex]-1+21i[/tex]Using the drawing find y: MzBDJ = 7y + 2, mZJDR = 2y + 7 * HRT O 25 O 19 O O TY
A quadratic equation is shown below:x^2 + 18x + 76 = 0Which of the following is the first correct step to write the above equation in the form (x-p)^2 = q, when p and q are integers? A. Add 9 to both sides of the equationB. Add 5 to both sides of the equationC. Subtract 5 from both sides of the equationD. Subtract 9 from both sides of the equation.
SOLUTION:
[tex]\begin{gathered} x^2\text{ + 18x + 76 = 0} \\ To\text{ make left hand p}\operatorname{erf}ect\text{ square, we add 5 to both sides} \\ x^2\text{ + 18x + 76 + 5 = 0 + 5} \\ x^2\text{ + 18x + 81 = 5} \\ x^2\text{ }+18x+9^2\text{ = 5} \\ (x+9)^2\text{ = 5} \end{gathered}[/tex]The correct option B, that is, add 5 to both sides of the equation.
if Sarah has 98 baseball cards in her collection for birthday her she's given 78 new cards and she sold 108 cards how many baseball cards does Sarah have left
68
1) Gathering the data
Sarah has 98 cards
She's given 78 then we can add
98 +78 = 176 cards
2) And right after that Sarah sold 108 cards, so now we can write
176 -108 = 68
3) Finally, Sarah now has 68 baseball cards left.
im using goformative to answer my question and I already did number 7 but the rest show my answer is incorrect so I will appreciate if I can get a help from you, I will paste the image of the work.
To get side QR we can use the the tangent function:
[tex]\begin{gathered} \tan 37=\frac{9}{QR} \\ QR=\frac{9}{\tan37} \\ QR=11.9 \end{gathered}[/tex]Now, to find PR we can use the sine function:
[tex]\begin{gathered} \sin 37=\frac{9}{PR} \\ PR=\frac{9}{\sin 37} \\ PR=15 \end{gathered}[/tex]Finally to find the remaining angle we have to remember that the interior angles of any triangle have to add to 180, then angle P is 53°.
2. Line ( has a slope of -7 and a y-intercept of 12. What is the equation for line in slope-intercept form? y =12x-7 y=-7x+12 --7x+12y=0which one of those equations are true
The general form of a straight line graph is: y = mx + c
where m and c are the slope and slope-intercept respectively.
from the question given, the slope (m) = -7
and the intercept (c) = 12
substituting the values into y = mx + c
then y = -7x + 12
Joey buys a home for $205,900. His home is predicted to increase in value 4% each year. What is the predicted value of his home in 22 years? Round answer to thenearest whole number
Since every year the value of the house increase by 4%, the new value will be the previous value plus 4% of the previous value. To find 4% of a quantity, we just have have to multiply it by 4 and then divide by 100(or, written as a decimal, multiply the number by 0.04).
If we call the previous value of the house as P and the new value as N, the new value after one year will be
[tex]N=P+0.04P=(1+0.04)P=1.04P[/tex]Every year that passes, to get the new value we multiply again by 1.04. The expression for the predicted value after t years is
[tex]N(t)=P_0(1.04)^t[/tex]Where P0 represents the initial value of the house. Evaluating t = 22 on this expression, we have
[tex]N(22)=205,900(1.04)^{22}=487,966.279171\ldots\approx487,966[/tex]The predicted value of his home in 22 years is $487,966.
Find the absolute change and the percentage change for the given situation.120 is decreased to 18
The absolute change is defined as:
[tex]V_2-V_1[/tex]where V1 and V2 are the initial and final values, respectively.
Plugging the values given we have that:
[tex]18-120=-102[/tex]Therefore the absolute change is -102. (The minues sign indicate a decrease)
The percentage change is given by:
[tex]\frac{V_2-V_1}{\lvert V_1\rvert}\cdot100[/tex]plugging the values given we have:
[tex]\frac{18-120}{\lvert120\rvert}\cdot100=-\frac{102}{120}\cdot100=-0.85\cdot100=85[/tex]Therefore the percentage change is -85% (Once again the minus sign indicate a decrease)
Hay e escalones desde el pedestal hasta la cabeza de la Estatua de la Libertad. La cantidad de escalones que hay en el Monumento a Washington es 27 menos que 6 veces la cantidad de escalones que hay en la Estatua de la Libertad. ¿Qué expresión representa la cantidad de escalones que hay en el Monumento de Washington en función de e? 27 < 6e 6(e-27) 6e-27 They 6e
Let
e -----> number of steps from the pedestal to the head of the Statue of Liberty
f ----> number of steps on the Washington Monument
we have that
f=6e-27
therefore
teh answer is
6e-27
Do you understand my explanation?escalones que hay en el Monumento a Washington
we have that
f=6e-27
The mean life of a television set is 97 months with the variance of 169. If a sample of 59 televisions is randomly selected what is the probability that the sample mean would be less than 100.9 months? Round your answer to four decimal places if necessary
Given that the mean life of a television set is 97 months, you can set up that:
[tex]\mu=97[/tex]You also know that the variance is:
[tex]\sigma^2=169[/tex]You can find the standard deviation by taking the square root of the variance. Then:
[tex]\sigma=\sqrt{169}=13[/tex]You need to find:
[tex]P(X<100.9)[/tex]You need to find the z-score with this formula:
[tex]z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Knowing that:
[tex]\bar{X}=100.9[/tex]You can substitute values into the formula and evaluate:
[tex]z=\frac{100.9-97}{\frac{13}{\sqrt{59}}}\approx2.30[/tex]You have to find:
[tex]P(z<2.30)[/tex]Using the Standard Normal Distribution Table, you get:
[tex]P(z<2.30)\approx0.9893[/tex]Then:
[tex]P(X<100.9)\approx0.9893[/tex]Hence, the answer is:
[tex]P(X<100.9)\approx0.9893[/tex]How do I solve for x? Would my answer be 27?
Given:
[tex]\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle XAC=(5x+13)^o[/tex][tex]We\text{ know that }\angle BAC\text{ and }\angle XAC\text{ are supplementary angles.}[/tex]The sum of the supplementary angles =180 degrees.
[tex]\angle BAC+\angle XAC=180^o[/tex][tex]\text{ Substitute }\angle XAC=(5x+13)^o\text{ in the equation.}[/tex][tex]\angle BAC+(5x+13)^o=180^o[/tex][tex]\angle BAC=180^o-\mleft(5x+13\mright)^o[/tex]We know that the sum of all three angles of the triangle is 180 degrees.
[tex]\angle ABC+\angle ACB+\angle BAC=180^o[/tex][tex]\text{ Substitute }\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle BAC=180^o-(5x+13)^o\text{.}[/tex][tex](4x+2)^o+(2x-9)^o+180^o-(5x+13)^o=180^o[/tex][tex](4x+2)^o+(2x-9)^o-(5x+13)^o=180^o-+180^o[/tex][tex](4x+2)^o+(2x-9)^o-(5x+13)^o=0[/tex][tex]4x+2+2x-9-5x-13=0[/tex]Adding like terms that have the same variable with the same powers.
[tex]4x+2x-5x+2-9-13=0[/tex][tex]x-20=0[/tex][tex]x=20[/tex]Hence the value of x is 20.
simplifying with like terms; a + 2a -7
In the expression like terms are a and 2a.
Simplify the expression
[tex]a+2a-7=3a-7[/tex]So answer is 3a - 7.
I have a pentagon that 8 and 8 and 6 and 6 and 10 whats the perimeter?
The perimeter of any closed figure is equal to sum of all sides of the figure.
Determine the perimeter of pentagon by addition of measure of sides of pentagon.
[tex]\begin{gathered} P=8+8+6+10+6 \\ =38 \end{gathered}[/tex]So answer is 38 cm.
L) Point A bisects CR. CA = 8x + 1 and AR = 6x+13.Find CA.34927
We will investigate some application of line bisectors.
We have a line segment denoted as ( CR ). A point ( A ) is said to be bisecting the line segment.
Line bisection involves the process of equally dividing the entire line segment in two equal halves! We can also represent this scenario graphically for clearification:
We can also represent line bisection mathematically in terms of two smaller divisions ( CA and AR ) as follows:
[tex]Bi\sec tion\colon\text{ |CA| = |AR| = }\frac{|CR|}{2}[/tex]Where, the quantities are expressed as magnitudes/lengths of each segment indicated.
We are given expressions for bifurcated line segments |CA| and |AR| in terms of variable ( x) as follows:
[tex]\begin{gathered} |CA|\text{ = 8x + 1} \\ |AR|\text{ = 6x + 13} \end{gathered}[/tex]Now we will use the expression given for each smaller division of line |CR| and plug it in the general " Bisection " expression developed above:
[tex]\begin{gathered} |CA|\text{ = |AR|} \\ 8x\text{ + 1 = 6x + 13} \end{gathered}[/tex]We have constructed an equation with a single variable ( x ). We can solve this equation for the variable ( x ) using basic mathematical operations as follows:
[tex]\begin{gathered} 8x\text{ - 6x = 13 - 1} \\ 2x\text{ = 12} \\ x\text{ = 6} \end{gathered}[/tex]Once we have solved for the variable ( x ). We will again use the defined expression for each smaller segments and determine the magnitudes as follows:
[tex]\begin{gathered} |CA|\text{ = 8}\cdot(6)\text{ + 1 } \\ |CA|\text{ = 49 units} \\ \\ |AR|\text{ = 6}\cdot(6)\text{ + 13 } \\ |AR|\text{ = 49 units} \\ \\ |\text{ CR | = 2}\cdot|CA|\text{ = 2}\cdot49 \\ |\text{ CR | = 98 units} \end{gathered}[/tex]Roberto bought a new graduated cylinder for his chemistry class. it holds 650 mililiters of liquid. if the cylinder has a radius of 5 cm, then how tall is the cylinder.
8.27 cm
Explanation
Step 1
the volume of a cylinder is given by:
[tex]\begin{gathered} \text{Volume}=\text{ area of the circle}\cdot\text{ height} \\ \text{Volume}=(\pi\cdot raidus^2)\cdot\text{height} \end{gathered}[/tex]then
Let
Heigth=unknown=h
volume=650 ml
radius= 5 cm
also
1 mililiter= 1 cubic centimeter
so,replacing
[tex]\begin{gathered} \text{Volume}=(\pi\cdot raidus^2)\cdot\text{height} \\ \text{650 }=(\pi\cdot(5cm)^2)\cdot\text{h} \\ 650=25\pi\cdot h \\ \text{divide both sides by 25 }\pi \\ \frac{650}{25\pi}=\frac{25\pi h}{25\pi} \\ h=\frac{650}{25\pi}=8.27\text{ cm} \end{gathered}[/tex]so, the cylinder is 8.27 cm tall.
I hope this helps you
What is the domain of the rational function f of x is equal to the quantity x squared plus x minus 6 end quantity over the quantity x cubed minus 3 times x squared minus 16 times x plus 48 end quantity question mark
To solve this problem, we have to find the zeros of the expression in the denominator, to do it, factor the expression:
[tex]\begin{gathered} x^3-3x^2-26x+48=0 \\ (x-3)(x-4)(x+4)=0 \\ x-3=0 \\ x=3 \\ x-4=0 \\ x=4 \\ x+4=0 \\ x=-4 \end{gathered}[/tex]The zeros of the function are x=3,4,-4.
Since these values make the expression be zero, they are not included in the domain of the function. This is because the expression in the denominator can not be zero, otherwise, the function would be undefined.
The correct answer is B:
[tex]\mleft\lbrace x\in R\mright|x\ne-4,3,4\}[/tex]There are 221 6th graders in the HPS district that are going on field trip to the Detroit Institute of Arts when we get back to school. If each bus holds 46 students, how many buses should be hierd to transport us?
Students = 221
Each bus holds 46 students
Divide the total number of students (221) by the capacity of each bus (46 )
221 /46 = 4.8 = 5 buses
Convert the unit to the specified equivalent unit round your answer to at least1 decimal place if necessary
Given:
There are given that the 209 ounces to convert into the decigram.
Explanation:
According to the concept:
To convert the ounces into the decigram, we need to multiply the mass values by 283.
That means,
The value of 1 ounce is 283 decigram
So,
[tex]\begin{gathered} 209ounces=209\times283decigram \\ =59147decigram \end{gathered}[/tex]Final answer:
Hence, the value of the 209 ounces is 59147 decigrams.
given triangle CAT is congruent to triangle DOG. Solve for x
Answer:
The value of x is 2 or -5.5.
Explanation:
Given that triangle CAT is congruent to triangle DOG, then we have that:
[tex]\angle T\cong\angle G[/tex]Step 1: We determine the value of angle T.
[tex]\begin{gathered} \angle T=180^0-(87^0+75^0) \\ =180^0-162^0 \\ =18^0 \end{gathered}[/tex]Step 2: Since angle T is congruent to angle G, then:
[tex](x+4)(2x-1)=18[/tex]Step 3: We solve the equation above for x.
[tex]\begin{gathered} 2x^2-x+8x-4-18=0 \\ 2x^2+7x-22=0 \\ 2x^2-4x+11x-22=0 \\ 2x(x-2)+11(x-2)=0 \\ (2x+11)(x-2)=0 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 2x+11=0\text{ or x-2=0} \\ 2x=-11\text{ or x=2} \\ x=-5.5\text{ or x=2} \end{gathered}[/tex]The value of x is 2 or -5.5.
A figure is made up of two triangles and a square. The trianglesand the square have the same base length of 9 feet. Thetriangles have a height of 12.3 feet. What is the total area of thefigure?
I need help with number 16 can I please get help?
We can break apart the figure into 4 separate figures and find the area of each of these individual figures. Then sum to get area of total figure.
We break apart the figure as shown below:
First,
Area of Triangle = 0.5 * base * height
Area of Rectangle = base * height
Now, let's find each of the Areas A through D:
Area of A:
To find the base of this triangle, we have to use pythagorean theorem. By which we can write:
[tex]b^2+4^2=6^2[/tex]Where b is the base. let's solve for b:
[tex]\begin{gathered} b^2+16=36 \\ b^2=36-16 \\ b^2=20 \\ b=\sqrt[]{20} \\ b=\sqrt[]{4}\sqrt[]{5} \\ b=2\sqrt[]{5} \end{gathered}[/tex]Area is
[tex]\begin{gathered} 0.5\cdot\text{base}\cdot\text{height} \\ =\frac{1}{2}\cdot2\sqrt[]{5}\cdot4 \\ =4\sqrt[]{5} \end{gathered}[/tex]Area of B:
This is a rectangle with base = 10 and height 4, so the area is:
Area = 4 * 10 = 40
Area of C:
Area of C is exactly same as area of B, base is 10 and height is 4. So,
Area = 4 * 10 = 40
Area of D:
Like area of A, we have to find the base of the triangle first, using pythagorean theorem. We can write:
[tex]\begin{gathered} b^2+4^2=4.5^2 \\ \end{gathered}[/tex]Solving for b:
[tex]\begin{gathered} b^2+4^2=4.5^2 \\ b^2+16=20.25 \\ b^2=\frac{17}{4} \\ b=\frac{\sqrt[]{17}}{\sqrt[]{4}} \\ b=\frac{\sqrt[]{17}}{2} \end{gathered}[/tex]Now, area of triangle is:
[tex]A=\frac{1}{2}(\frac{\sqrt[]{17}}{2})(4)=\sqrt[]{17}[/tex]Area of whole figure:
[tex]\begin{gathered} 4\sqrt[]{5}+40+40+\sqrt[]{17} \\ =80+4\sqrt[]{5}+\sqrt[]{17} \end{gathered}[/tex]Since mulch costs $3 per square feet, we have to multiply the area by "3", so we have:
[tex]3\times(80+4\sqrt[]{5}+\sqrt[]{17})\approx279.202[/tex]It will cost around:
$279.20
What is the average rate of change of the equation f(x)^2+3x-5 from x=2 to x=4?Type your numerical answer below. Use the hyphen (-) to represent a negative sign if necessary.
Given:
The equation is,
[tex]f\mleft(x\mright)=x^2+3x-5,x=2\text{ to x = 4}[/tex]To find: The average rate of change
Explanation:
The average rate of the change formula is,
[tex]A\left(x\right)=\frac{f\mleft(b\mright)-f\mleft(a\mright)}{b-a}[/tex]Here, we have
[tex]\begin{gathered} a=2 \\ b=4 \end{gathered}[/tex]Substituting we get,
[tex]\begin{gathered} A\lparen x)=\frac{f\mleft(4\mright)-f\mleft(2\mright)}{4-2} \\ =\frac{\left\lbrack4^2+3\left(4\right)-5\right?-\left\lbrack2^2+3\left(2\right)-5\right?}{2} \\ =\frac{16+12-5-\left\lbrack4+6-5\right\rbrack}{2} \\ =\frac{23-5}{2} \\ =\frac{18}{2} \\ =9 \end{gathered}[/tex]Final answer:
The average rate of change of the given equation is 9.
the letter "t" estimated makes up 10% of a language. a random sample of 700 letters is taken from a book. what is the approximate probability that the random sample of 700 letters will contain 8.9% t's
In this problem, we have a Binomial Probability Distribution
so
n=700
x=700*(8.9/100)=62.3=62
[tex]P(x=62)=\frac{700!}{62!(700-62)!}\cdot0.10^{(62)}\cdot0.90^{(700-62)}[/tex]P(x=62)=0.0313
the aprroximate probability is 3.13%Your credit card charges 16.5% interest on any unpaid balance. If your credit card balance forthe month is $650, how much will you be charged in interest and what will your new balancebe?
Solve for interest
[tex]\begin{gathered} \text{convert the rate first from percentage to decimal} \\ 16.5\%\rightarrow0.165 \\ \\ \text{Then multiply it to the balance to get the interest} \\ \$650\times0.165=\$107.25 \\ \\ \text{Therefore, the interest is \$107.25} \end{gathered}[/tex]Solve for new balance.
[tex]\begin{gathered} \text{Add the interest the the credit card balance to get the new balance.} \\ \$650+\$107.25=\$757.25 \\ \\ \text{Therefore, the new balance will be \$757.25} \end{gathered}[/tex]At a food drive, afood bank has a goal to collect 24,000 cans.If the food bank collects 100 fewer cansthan its goal, how many cans did it collect?
Given:
• Expected number of cans to collect = 24,000 cans.
,• The food bank collects 100 fewer cans.
Let's find the number of cans it collected.
Since the food bank collected 100 fewer cans, to find the number of cans it collected, let's subtract 100 from the expected goal which is 24000 cans.
Hence, we have:
Number of cans collected = expected goal - 100
Number of cans collected = 24000 - 100 = 23900
Therefore, the number of cans the food bank collected was 23,900 cans.
ANSWER:
23900 cans