Given that the associative property of multiplication says that you can group the numbers in any combination, we can reorganize the expression as: 7·(10·3)=210. So the answer would be the first option.
if you draw one card at random what is the probability that card is a 7 out of diamonds
Assuming that all the cards have the same probability of being randomly drawn, we conclude that the probability is:
P = 1/52 = 0.019
How to get the probability?We assume all the cards have the same probability of being randomly drawn.
Then the probability of drawing the card 7 of diamonds will be equal to the quotient between the number of 7 of diamonds in the deck (there is only one) and the total number of cards in the deck (52).
P = 1/52 = 0.019
The probability is 0.019
Learn more about probability:
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What is the answer to 9m^2-66m+21=0
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Write the given quadratic equation.
[tex]9m^2-66m_{}+21=0[/tex]STEP 2: Write the quadratic formula
[tex](m_1,m_2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]STEP 3: Solve the given equation using the quadratic formula
[tex]\begin{gathered} 9m^2-66m_{}+21 \\ \text{From the }equation, \\ a=9,b=-66,c=21 \\ m_{1,\: 2}=\frac{-\left(-66\right)\pm\sqrt{\left(-66\right)^2-4\cdot\:9\cdot\:21}}{2\cdot\:9} \\ Simplify\sqrt[]{(-66)^2-4\cdot\: 9\cdot\: 21} \\ \sqrt[]{(-66)^2-4\cdot\: 9\cdot\: 21}=\sqrt[]{4356-756}=\sqrt[]{3600}=60 \\ \\ m_{1,\: 2}=\frac{-\left(-66\right)\pm\:60}{2\cdot\:9} \\ Separate\: the\: solutions \\ m_1=\frac{-\left(-66\right)+60}{2\cdot\:9},\: m_2=\frac{-\left(-66\right)-60}{2\cdot\:9} \\ m_1=\frac{-(-66)+60}{2\cdot\: 9}=\frac{66+60}{18}=\frac{126}{18}=7 \\ \: m_2=\frac{-(-66)-60}{2\cdot\: 9}=\frac{66-60}{18}=\frac{6}{18}=\frac{1}{3} \end{gathered}[/tex]Hence, the answer to the given quadratic equation is:
[tex]\begin{gathered} m=7 \\ m=\frac{1}{3} \end{gathered}[/tex]In the accompanying diagram of right trianglesABD and DBC, AB = 5, AD = 4, and CD=1. Findthe length of BC, to the nearest tenth.B54DYour answerI
Consider the triangle ABD.
Determine the length of side BD by using pythagoras theorem.
[tex]\begin{gathered} (BD)^2=(AB)^2-(AD)^2 \\ BD=\sqrt[]{(5)^2-(4)^2} \\ =\sqrt[]{9} \\ =3 \end{gathered}[/tex]Consdier the triangle BDC.
Determine the length of side BC using pythagoras theorem.
[tex]\begin{gathered} (BC)^2=(BD)^2-(CD)^2 \\ BC=\sqrt[]{(3)^2-(1)^2} \\ =\sqrt[]{9-1} \\ =\sqrt[]{8} \\ =2.828 \\ \approx2.8 \end{gathered}[/tex]Thus length of sdie BC is 2.8.
gotta double check a Answer
Solution
For this case we have the following relationship given:
R90° ccw r y=x
And for this case we can conclude that the best answer is:
90 degree counterclockwise rotation about the origin
) What is the vertical asymptote for the rational function f(x)2x-523x + 6A) X = 2BB) x = }3.(x = -2D)x=-D56.
Answer:
C. x=-2
Explanation:
Given the rational function:
[tex]f(x)=\frac{2x-5}{3x+6}[/tex]To find the vertical asymptote of f(x), set the denominator of f(x) equal to 0 and solve for x:
• Denominator of f(x) =3x+6
Solve for x:
[tex]\begin{gathered} 3x+6=0 \\ 3x=-6 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}=-\frac{6}{3} \\ x=-2 \end{gathered}[/tex]The vertical asymptote of f(x) is x=-2.
Option C is correct.
What is the value of x that satisfies the equation í (& - 2(1 - 2) = $ (+2)
Let's start clearing the value of x
[tex]\begin{gathered} 2(\frac{x}{2}-2)=3\cdot\frac{4}{3}(\frac{x}{3}+2) \\ 2(\frac{x}{2}-2)=4(\frac{x}{3}+2) \end{gathered}[/tex]Now we are going to multiply to open the parenthesis
[tex]\begin{gathered} 2\cdot\frac{x}{2}-2\cdot2=4\cdot\frac{x}{3}+4\cdot2 \\ x-4=\frac{4x}{3}+8 \\ \frac{4x}{3}-x=-4-8 \\ \frac{x}{3}=-12 \\ x=-12\cdot3 \\ x=-36 \end{gathered}[/tex]HomeHumber of newspapers070009PaulGaryValentinaOlivia904What is the mean of this data setWhat is the median of this data setiWhat is the mode of this datasetit more than one mode enter them in order from least to greatest, separated bycommes, and no spaces. If there is no mode, put NAWhat is the range of this dataset
Answer:
[tex]undefined[/tex]Explanation:
Given the data on the table, let us arrange from least to the greatest.
[tex]84,86,89,97,98,98[/tex]The mean is the sum of all the data divided by the number of data;
[tex]\begin{gathered} \operatorname{mean}=\frac{84+86+89+97+98+98}{6} \\ \operatorname{mean}=\frac{552}{6} \\ \operatorname{mean}=92 \end{gathered}[/tex]The median is the middle number (the average of the middle numbers);
[tex]\begin{gathered} \operatorname{median}=\frac{89+97}{2} \\ \operatorname{median}=\frac{186}{2} \\ \text{median}=93 \end{gathered}[/tex]The mode is the highest occurring number;
[tex]\text{mode}=98[/tex]The range is the difference between the greatest and the least number.
[tex]\begin{gathered} \text{greatest number = 98} \\ \text{least number = 84} \\ \text{Range = 98 - 84} \\ \text{Range =14} \end{gathered}[/tex]How does the graph of g(x)= 2^x+3differ from the graph of f(x) = 2^xАIt is moved up 3 unitsBIt is moved down 3 unitsCIt is moved right 3 units+DIt is moved left 3 units
About 51% of U.S. college students are below 25 years old. About 24% of U.S. college students are above 34 years old. What is the probability that a U.S. college student chosen at random is below 25 or above 34 years?0.760.740.751.75
Answer
0.75
Explanation
The probability that a U.S college student chosen at random is below 25 years is:
[tex]\begin{gathered} =51\text{ \%} \\ =\frac{51}{100}=0.51 \end{gathered}[/tex]The probability that a U.S college student chosen at random is above 34 years is
Now, by addition law of probability, the probability that a U.S college student chosen at random is below 25 or above 34 years would be
[tex]\begin{gathered} 0.51+0.24 \\ =0.75 \end{gathered}[/tex]- Solve 2cos (3x) - 1 = 0 on the interval [0, 21).T 77 97 151 177 23T12' 12' 12' 12 12'12T7T4' 4No solutionT 137 251 111 231 35718' 18 18 '18 18 1899
Let's solve the trig equation >>>
[tex]\begin{gathered} \sqrt[]{2}\cos (3x)-1=0 \\ \sqrt[]{2}\cos (3x)=1 \\ \cos (3x)=\frac{1}{\sqrt[]{2}} \\ 3x=\frac{\pi}{4},\frac{7\pi}{4} \\ x=\frac{\pi}{12},\frac{7\pi}{12} \end{gathered}[/tex]To get the other angles within 2π, we add 2π to these two angles. Thus,
[tex]undefined[/tex]What is the solution of the inequality shownbelow?w +4 _<-1The less than is underlined and it’s throwing me off
We will solve as follows:
[tex]w+4\le-1\Rightarrow w\le-5[/tex]What is true about the function f(x) = -3|x+2| - 1 ?A) It has a Maximum at -1 when x=2B) It has a Minimum at -1 when x=-2C) It has a Maximum at -1 when x=-2D) It has a Minimum at -1 when x=2
First we will graph the function,
So we have a maximum at -1 when x = -2
Save Sub Hillery condujo 96 millas hoy. Bob llevó medio a todos los que Hillery. Cuántas millas conducen combinado? GO A) 120 B) 144 ) 192 D) 288 Expressions and Equat
Hillery condujo 96 millas hoy.
También sabemos que Bob condujo la mitad de lo que condujo Hillery, es decir, 96/2 = 48
En total, los dos condujeron 96 + 48 = 144 millas
Respuesta:
B) 144
The graph of the exponential function f(x)=3^x+3 is given with three points. Determine the following for the graph of f^-1(x).1. Graph f^-1(x)2. Find the domain of f^-1(x)3. Find the range of f^-1(x)4. Does f^-1(x) increase or decrease on its domain?5. The equation of the vertical asymptote for f^-1(x) is?
Let's begin by listing out the given information:
[tex]\begin{gathered} f\mleft(x\mright)=3^x+3\Rightarrow y=3^x+3 \\ Switch\text{ }the\text{ }variables\text{ x \& y in the equation, we have:} \\ x=3^y+3\Rightarrow x-3=3^y \\ x-3=3^y\Rightarrow3^y=x-3 \\ \text{Take the }ln\text{ }o\text{f both }sides\text{, we have:} \\ y=\frac{\ln{\left(x - 3 \right)}}{\ln{\left(3 \right)}} \\ y=f^{-1}\mleft(x\mright) \\ f^{-1}\mleft(x\mright)=\frac{\ln{(x-3)}}{\ln{(3)}} \\ \end{gathered}[/tex]2.
The domain of a function is the set of input or argument values for which the function is real and defined. This is given by:
[tex]\begin{gathered} x-3;x>3 \\ \therefore x>3 \end{gathered}[/tex]3.
The range of a function is the set of output values for which the function is defined. This is given by:
[tex]\begin{gathered} 3^x+3\colon-\infty\: 4.The range of f(x) is the domain of f^-1(x) since they are inverse of one another.
[tex]\begin{gathered} f\mleft(x\mright)=3^x+3 \\ x=0 \\ f(0)=3^0+3=1+3=4 \\ x=1 \\ f(1)=3^1+3=3+3=6 \\ x=2 \\ f(2)=3^2+3=9+3=12 \\ \end{gathered}[/tex]Therefore, the domain of f^-1(x) increases
5.
The asymptote of a curve is a line such that the distance between the curve and the line approaches zero
[tex]\begin{gathered} \: \frac{\ln\left(x-3\right)}{\ln\left(3\right)}\colon\quad \mathrm{Vertical}\colon\: x=3 \\ \therefore x=3 \end{gathered}[/tex]20 grams of table sugar has a density of 1.59 what is the volume of the sample
Problem
20 grams of table sugar has a density of 1.59 what is the volume of the sample
Solution
For this case we can use the definition of density:
d= m/v
And if we solve for v we got:
v= m/d
And replacing we got:
v= 20/1.59= 12.58
Which of the following equations describes the line shownbelow? Check all that apply.6((-6,2)(-1,-4)
First, we have to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=-6 \\ x_2=-1 \\ y_1=2 \\ y_2=-4 \end{gathered}[/tex][tex]m=\frac{-4-2}{-1-(-6)}=\frac{-6}{-1+6}=\frac{-6}{5}=-\frac{6}{5}[/tex]This means A and B represent the line because they use the same slope and the same coordinates.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=-\frac{6}{5}(x+6) \\ y+4=-\frac{6}{5}(x+1) \end{gathered}[/tex]Which inequality does NOT represent thecorrect position of two numbers on a numberline? A 41/2 > 25/4B -41/2 > -25/5C -6 < -5D -1/2 < 1/2
4 1/2 > 25/4 (option A)
Explanation:To determine the inequality not in the correct positin, we will change the fractions to decimals. That way it is easy to compare:
[tex]\begin{gathered} a)\text{ 4}\frac{1}{2}\text{ > }\frac{25}{4} \\ \text{4}\frac{1}{2}\text{ > 6}\frac{1}{4} \\ 4.5\text{ > 6.25} \\ 4.5\text{ is less than 6.25 not greater than as s}en\text{ in the question} \\ \text{Hence, this is the incorrect one} \end{gathered}[/tex][tex]\begin{gathered} b)-4\frac{1}{2}\text{ > }\frac{-25}{5} \\ -4.5\text{ > -5} \\ \text{For negative numbers, the smaller numbers are greater than the bigger numbers} \\ \text{This is correct} \end{gathered}[/tex][tex]\begin{gathered} -6\text{ < -5} \\ \text{For negative numbers, the smaller numbers are greater than the bigger numbers} \\ \text{this is correct} \end{gathered}[/tex][tex]\begin{gathered} d)\text{ }\frac{-1}{2}\text{ < }\frac{1}{2} \\ -0.5\text{ < 0.5} \\ \text{Negative numbers are less than positive numbers} \\ \text{This is correct} \end{gathered}[/tex]I need help with this practice problem It asks to answer (a) and (b) Please put these separately so I can see which is which
We have a series:
[tex]\sum ^{\infty}_{n\mathop{=}1}a_n=\sum ^{\infty}_{n=1}(\frac{2n!}{2^{2n}})\text{.}[/tex](a) The value of r from the ratio test is:
[tex]\begin{gathered} r=\lim _{n\rightarrow\infty}|\frac{a_{n+1}}{a_n}| \\ =\lim _{n\rightarrow\infty}\frac{\frac{2(n+1)!}{2^{2(n+1)}}}{\frac{2n!}{2^{2n}}} \\ =\lim _{n\rightarrow\infty}\frac{2(n+1)!\cdot2^{2n}}{2n!\cdot2^{2(n+1)}^{}} \\ =\lim _{n\rightarrow\infty}\frac{2(n+1)\cdot n!\cdot2^{2n}}{2n!\cdot2^{2n}\cdot2^2} \\ =\lim _{n\rightarrow\infty}\frac{(n+1)}{2^2} \\ =\infty. \end{gathered}[/tex](b) Because r = ∞ > 1, we conclude that the series is divergent.
Answer
(a) r = ∞
(b) The series is divergent.
Mr Sanders wants to display his American flag in a triangular case as shown below what is the area of this triangular case
Solution
For this case we have a triangle with the following dimensions:
b= 14 2/5 = 72/5 = 14.4 in represent the base
h= 8.5 in represent rhe height
And the area is given by:
[tex]A=\frac{b\cdot h}{2}=\frac{14.4\cdot8.5}{2}=61.2in^2[/tex]Then the final answer is 61.2 in^2
What is the volume of this rectangular Pyramid picture to follow
SOLUTION:
Case: Rectangular pyramid
Method:
The base has a dimension 5mm by 5mm
The height is 3mm
The Volume, therefore:
[tex]\begin{gathered} V=\frac{1}{3}\times l\times w\times h \\ V=\frac{1}{3}\times5\times5\times3 \\ V=\frac{75}{3} \\ V=25mm^3 \end{gathered}[/tex]Final answer:
The volume, V= 25 cubic millimeters
what is y? i understood every question before this one, i think i maybe typing the answer wrong can you clarify what y is
Answer:
[tex]y\text{ = 7}\sqrt{6}[/tex]Explanation:
Here, we want to get the value of y
What we have in the triangle is an isosceles right triangle (two of the internal angles are 45 degrees each)
Thus, we have the base equal to the height
To get the hypotenuse length, we use Pythagoras' theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides
Thus, we have it that:
[tex]\begin{gathered} \text{ y}^2\text{ = \lparen7}\sqrt{3\text{ }})\placeholder{⬚}^2\text{ + \lparen7}\sqrt{3}\text{ \rparen}^2\text{ } \\ y^2\text{ =147+ 147} \\ y^2\text{ = 294} \\ y\text{ = }\sqrt{294} \\ y\text{ = 7}\sqrt{6} \end{gathered}[/tex]Determine the x intercepts of the polynomial function: f(x)=x^4-x^2 Recall that the x intercept is a point (x,0) where our value for y is always zero. List the intercepts (x,0) from smallest to largest and separate them with a comma between each point.Answer:
To find such x intercepts, we make our y-value 0 and solve for x as following:
[tex]\begin{gathered} f(x)=x^4-x^2 \\ \rightarrow x^4-x^2=0 \\ \rightarrow(x^2)(x^2-1)=0 \\ \rightarrow(x^2)(x+1)(x-1)=0 \\ \\ x^2=0\rightarrow x_1=0 \\ \\ x+1=0\rightarrow x_2=-1 \\ \\ x-1=0\rightarrow x_3=1 \end{gathered}[/tex]This way, we can conclude that the x intercepts are:
-1,0,1
18 8 12 8 4 13 what is the median & mean
The Median is 10
The mean is 10.5
Explanation:To find the median, we need to arrange the data in an ascending or descending order.
In an ascending order, we have:
4, 8, 8, 12, 13, 18
The median is the middle number.
Since the number of data is even, the median is the mean of the two middle numbers.
The two middle numbers are: 8 and 12
The mean is (8 + 12)/2 = 20/2 = 10
The median is 10
The mean of the data is the sum of the data divided by the number of data.
The sum of data is:
4 + 8 + 8 + 12 + 13 + 18 = 63
The number of data is 6
Mean = 63/6 = 10.5
Venus is approximately 1.082×107
To express the number in standard notation we need to move the decimal point 9 times to the right, then:
[tex]1.082\times10^9=1,082,000,000[/tex]Therefore the answer is d
Mathematical patterns: Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
Solution
Step-by-step explanation:
We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.
Let the first five terms of a sequence be 5, 10, 20, 40 and 80
These terms are taken from a geometric sequence with first term
[tex]a_15,r=2[/tex]first term a = 5
common ratio r = 2
Therefore, we have
[tex]\begin{gathered} a_2=a_1\times r \\ a_3=a_2\times r \end{gathered}[/tex]Therefore, the recursive formula is
[tex]\begin{gathered} a_{n+1}=2a_n \\ a_1=5 \end{gathered}[/tex]And explicit formula is
[tex]a_n=a_1r^{n-1}[/tex]what is 15 what is 15 - 3/10
15 - 3/10 = ?
convert 3/10 to decimal:
So, 3/10 = 0.3
So,
15 - 3/10 = 15 - 0.3 = 15.0 - 0.3 = 14.7
In the function y+ 3 = (2x) + 1, what effect does the number 2 have on the graph, as compared to the graph of 1=1? 2 A. It shrinks the graph horizontally to 1/2 the original width B. It shrinks the graph vertically to 1/2 the original height. O C. It stretches the graph horizontally by a factor of 2. D. It stretches the graph vertically by a factor of 2
The given transformation f(2x) represents a horizontal compression by a scale factor of 1/2.
Therefore, the right answer is A.which funtion has the largest value for f(-3)?. f(x)=2-4x. f(x)=2x-5. f(x)=6-3^x. f(x)=2^×+10
The notation f(-3) indicates that you have to calculate the value of the function f(x) for x=3.
To determine which value has the largest value for f(-3) you have to replace each function with x=3 and calculate the corresponding value of f(x)
1.
[tex]\begin{gathered} f(x)=2-4x \\ f(-3)=2-4(-3) \\ f(-3)=2-(-12) \\ f(-3)=2+12 \\ f(-3)=14 \end{gathered}[/tex]2.
[tex]\begin{gathered} f(x)=2x-5 \\ f(-3)=2\cdot(-3)-5 \\ f(-3)=-6-5 \\ f(-3)=-11 \end{gathered}[/tex]3.
[tex]\begin{gathered} f(x)=6-3^x \\ f(-3)=6-3^{-3} \\ f(-3)=\frac{161}{27} \\ f(-3)\approx5.92 \end{gathered}[/tex]4.
[tex]\begin{gathered} f(x)=2^x+10 \\ f(-3)=2^{-3}+10 \\ f(-3)=\frac{81}{8} \\ f(-3)\approx10.125 \end{gathered}[/tex]Now that we calculated f(-3) for each one of the functions, you can compare them.
The function that has the largest value of f(-3) is the first one: f(x)=2-4x
find the measure of angle cdb. explain your reasoning including the postulate you used. find the measure of angle abd. find the measure of angle a.
We get that the triangles ADB and CDB are congruent because of SSS(Side, Side, Side postulate) . So we get that the angles are also congruents
[tex]\begin{gathered} \angle ADB+\angle CDB=72^{\circ} \\ \end{gathered}[/tex]But ADB and CDB are the same so
[tex]\angle CDB=\frac{72}{2}=36^{\circ}[/tex][tex]\begin{gathered} \angle ABD=\angle CBD \\ 2\angle CBD=180 \\ \angle CBD=90^{\circ} \end{gathered}[/tex]The angle A is equal to
[tex]\angle A=180-90-36=54^{\circ}[/tex]Which of the following equations represent relationships where y is a linear function of x? SELECT ALL THAT APPLY A)2x + 3y = 6B)Y = 5C)X = 1D)y = 10 - xE)y = x^2 + 5x + 6F)y = -x
D) and F)
Explanation
Step 1
a linear function has 1 as the exponent of the variable, so we can discand option E)
Step 2
y is a function of x, it means that y depends on x ,
then, the equations that fit this
[tex]\begin{gathered} f(x)=y \\ y=f(x) \\ D)\text{ y=10-x} \\ F)y=-x \end{gathered}[/tex]D) and F), because B and C does not depend on x
I hope this helps you