Answer:
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What is the first step in solving the equation x2 - 25 = 0?
What is the second step in solving the equation?
Answer:
first step - make x² the subject of the formula
x² = 25
second step :
find the square root of both sides
√x² = √25
x = 5
Step-by-step explanation:
Let be the set of permutations of whose first term is a prime. If we choose a permutation at random from , what is the probability that the third term is equal to
Answer:
[tex]Pr = \frac{1}{6}[/tex]
Step-by-step explanation:
Given
[tex]S = \{1,2,3,4,5\}[/tex]
[tex]n = 5[/tex]
Required
Probability the third term is 3
First, we calculate the possible set.
The first must be prime (i.e. 2, 3 and 5) --- 3 numbers
[tex]2nd \to 4\ numbers[/tex]
[tex]3rd \to 3\ numbers[/tex]
[tex]4th \to 2\ numbers[/tex]
[tex]5th \to 1\ number[/tex]
So, the number of set is:
[tex]S = 3 * 4 * 3 * 2 * 1[/tex]
[tex]S = 72[/tex]
Next, the number of sets if the third term must be 2
[tex]1st \to 2[/tex] i.e. 1 or 5
[tex]2nd \to 3\ numbers[/tex] ---- i.e. remove the already selected first term and the 3rd the compulsory third term
[tex]3rd \to 1\ number[/tex] i.e. the digit 2
[tex]4th \to 2\ numbers[/tex]
[tex]5th \to 1\ number[/tex]
So
[tex]r = 2 * 3 * 1 * 2 * 1[/tex]
[tex]r = 12[/tex]
So, the probability is:
[tex]Pr = \frac{r}{S}[/tex]
[tex]Pr = \frac{12}{72}[/tex]
[tex]Pr = \frac{1}{6}[/tex]
Please help me with this question.
Answer:
Step-by-step explanation:
-1 ≤ x < 3 Solution set = {-1, 0 ,1 , 2}
-2 < x < 2 Solution set = {-1 , 0 , 1}
Integer values that satisfies both inequalities are -1 , 0 , 1
I \\\\\\\\\ I
[-1] -3 I \\\\\\\\\\\ I -2 2 [tex]\displaystyle\bf x\in[-1;2)\\-1;0;\underline1\\\\Answer: 1[/tex]
If each of the n production workers in a factory assembles one instrument every t minutes, how many instruments does the factory assemble in 7.5 hours of production
Answer:
The number of instruments assembled in 7.5 hours are 450 n/t.
Step-by-step explanation:
The number of instruments assembled in t minutes = n
the number of instruments assembled in 1 minute = n / t
Total time = 7.5 hours = 7.5 x 60 = 450 minutes
So, the number of instruments assembled in 450 minutes are
[tex]\frac{n}{t}\times 450\\\\\frac{450 n}{t}[/tex]
Help and explain pls and ty
Answer:
(g ○ f)(3) = 23
Step-by-step explanation:
Evaluate f(3) then substitute the value obtained into g(x)
f(3) = 2(3) + 4 = 6 + 4 = 10 , then
g(10) = 3(10) - 7 = 30 - 7 = 23
A group of 80 frogs was observed. The mean distance of their hops is 69 inches with a standard deviation of 3.5 inches. How many frogs would you expect to jump more than 72.5 inches?
Hello,
[tex]z=\dfrac{X-69}{3.5} \\\\For\ X=72.5, \\\\z=\dfrac{72.5-69}{3.5} =1\\[/tex]
Using table of a normal reduced law:
p(z≤1)=0.8413
Thus p(z≥1)=1-0.8413=0.1587
There are 80*0.1587=12.696 ≈13 (frogs)
Answer:
12 frogs
Step-by-step explanation:
Hello,
Using table of a normal reduced law:
p(z≤1)=0.8413
Thus p(z≥1)=1-0.8413=0.1587
There are 80*0.1587=12.696 ≈12 (frogs) you don't round up because you cant have .7 percent of a frog.
ps. I copy and pasted caylus's response but corrected their answer because it was correct except the rounding up part.
---------please help asap---- ---------------
Answer:
Question 1:
SAT average divided by budget per student and
SAT average divided by teachers per student
Question 2:
Yes. According to both definitions, school A has the higher SAT average relative to the resources invested per student.
environment is not ___ uniform all form
environment is not natural uniform all from
x/3 + 8 = 23 . Find the value of x
Answer:
45
Step-by-step explanation:
x/3 + 8 =23
=> x/3 = 23-8
=> x/3 = 15
=> x = 15 x 3
x = 45
Answer:
x=45
Step-by-step explanation:
To find x isolate the variables by using the properties of equality. First, subtract 8 from both sides, [tex]\frac{x}{3} = 15[/tex]. Then multiply both sides by 3, [tex]x=45[/tex]. Finally, to check you can plug 45 back into the equation, [tex]\frac{45}{3} +8=23[/tex]. Next, solve this equation and get 23=23, since this is a true statement 45 is correct.
In parallelogram BCDE if m
C
B
70
50°
E
Answer:
[tex]x=130[/tex]
Step-by-step explanation:
Opposite angles of a parallelogram are equal
EBC = 50° while, CDE = 50° too
Area of a parallelogram is 360°
Suppose, BCD to be x too, & form an equation:
[tex]50+50+x+x=360[/tex]
[tex]100+2x=360[/tex]
[tex]2x=360-100[/tex]
[tex]2x=260[/tex]
[tex]x=260/2[/tex]
[tex]x=130[/tex]
{CHECK: [tex]130+130+50+50=360^{o}[/tex]}
Answer:
m∠DEB = 130°
Step-by-step explanation:
Key: Only two angles are congruent because of the parallelogram
Since m∠EBC = 50° m∠CDE = 50°
Then we are missing m∠BCD and m∠DEB
50 + 50 + m∠BCD + m∠DEB = 360°
100 + m∠BCD + m∠DEB = 360°
m∠BCD + m∠DEB = 360 - 100
m∠BCD + m∠DEB = 260
m∠BCD + m∠DEB = 260/2
m∠BCD + m∠DEB = 130°
m∠BCD and m∠DEB = 130°
Nicole invested $1600 in an account that pays 4.75% interest compounded annually Assuming no deposits or withdrawals are made, find how much money Nicole would have in the account 18 years after her initial investment. Round to the nearest tenth (if necessary ).
Answer:
2968
Step-by-step explanation:
= O EQUATIONS AND INEQUALITIES Solving a decimal word problem using a linear equation of the... Jayden Esp Leila received a $90 gift card for a coffee store. She used it in buying some coffee that cost $7.26 per pound. After buying the coffee, she had $60.96 left on her card. How many pounds of coffee did she buy?
Answer:
Jayden buys 4 pounds of coffee
Step-by-step explanation:
Let's say that p represents the number of pounds of coffee Jayden bought. She starts with $90, and for each pound she buys, she loses $7.26 dollars. Therefore, as she loses 7.26 dollars, we must subtract the amount she pays from $90. Then, as she loses 7.26 dollars for each pound, we multiply 7.26 by the number of pounds to find the money she spends.
We can thus write our equation as
90 - 7.26*p = final amount = 60.96
90-7.26p = 60.96
subtract 90 from both sides to isolate the p and its coefficient
-7.26p = -29.04
divide both sides by -7.26 to isolate the p
p = 4
Jayden buys 4 pounds of coffee
Find the measure of the third angle of a triangle if the measures of the other two angles are given.
31.8 and 89.8
The three angles of a triangle equal 180
Third angle = 180 - 31.8 - 89.8 = 58.4
Answer: 58.4
Plis help me it’s for today
Answer:
Following are the solution to the given points:
Step-by-step explanation:
For question 1:
[tex]\to 3^{-4}= \frac{1}{3^4}=\frac{1}{81}=0.0123456789[/tex]
For question 2:
[tex]\to (-2)^{3}\cdot(-2)^{4}\cdot(-2)^{-1}=-8\cdot-16\cdot -\frac{1}{2}= 128\cdot -\frac{1}{2}=-64[/tex]
For question 3:
[tex]\to 7^{-4} \div 7^{-2}= \frac{1}{7^{4}} \div \frac{1}{7^{2}}=\frac{1}{7^{4}} \times \frac{7^{2}}{1}=\frac{1}{7^{2}} =\frac{1}{49} =0.0204081633[/tex]
For question 4:
[tex]\to [(-3)^{2}]^3= (-3)^{2\cdot 3}= (-3)^{6}=729[/tex]
For question 5:
[tex]\to [5 \cdot (-3)]^{2}= 25 \cdot 9=225[/tex]
For question 6:
[tex]\to [(10 \div 5)]^{3}= [(\frac{10}{5})]^{3}=[2]^{3}=8[/tex]
For question 7:
[tex]\to 10^6 \cdot 10^{-4} \cdot 10^2= 10^6 \cdot \frac{1}{10^{4}} \cdot 10^2= 10^2 \cdot 10^2=10^4=10,000[/tex]
For question 8:
[tex]\to (-4)^{-5}=\frac{1}{(-4)^{5}}=- \frac{1}{1,024}=-0.0009765625[/tex]
For question 9:
[tex]\to \frac{2^3}{2^4}= \frac{8}{16}=\frac{1}{2}=0.5[/tex]
For question 10:
[tex]\to (-6)^3 \cdot (-6)^5 \cdot (-6)^{-5}= (-6)^3 \cdot (-6)^5 \cdot \frac{1}{(-6)^{5}}= (-6)^3 =-216[/tex]
Find the sum of the Arithmetic series
2+5+8+............20th term
Which should equal 105° to prove that f I g?
abcd
Answer:
Step-by-step explanation:
sorry bout the poor drawing but it should be legible
Elana runs for 28 seconds and finishes at 250 meters .what is her velocity
Answer:
8.9m/s
Step-by-step explanation:
Time= 28s
Displacement= 250m
Velocity=?
Velocity (v) = displacement (d)/ Time (t)
V= 250/28
V=8.9m/s
OR YOU CAN APPROXIMATE IT
V=8.928
YOU CAN APPROXIMATE IT TO
V=8.93m/s
If the length of a is 6, the length of b is 4, and the length of c is 7, what is the measure of angle B
Answer:
B = 34.77°
Step-by-step explanation:
For this problem you are given all three side lengths and asked to find an angle. To do this you can use the law of cosines which is written:
[tex]b^{2} =a^{2} +c^{2} -2ac Cos(B)[/tex]
This can be rearranged to find the angle B:
[tex]b^{2} -a^{2} -c^{2} /-2ac = Cos(B)[/tex]
With lowercase letters being sides and uppercase being angles.
We simply plug in the sides and solve:
[tex]4^{2} -6^{2} -7^{2}/-2*6*7= Cos(B)[/tex]
0.8214 = Cos (B)
Then you use inverse cosine to get angle B alone.
B = 34.77°
hallar "x"
...................................
In a carnival game called Spot the Spot, the player has to drop five disks onto a red circle. The disks must cover it completely for the player to win. The probability that a skilled player can drop one of the disks onto the exact place on the red circle that it must occupy is about 1/3. What is the probability that such a player will be able to drop
Answer:
See explanation
Step-by-step explanation:
Given
[tex]n=5[/tex] --- disks
[tex]p = \frac{1}{3}[/tex] --- success probability
Required
The question is incomplete, as the required probability is not stated.
However, the question follows binomial distribution and the probability is calculated using:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
Assume the question requires that we calculate the probability that he's able to drop 2 disks, the probability will be:
[tex]P(x = 2) = ^5C_2 * (\frac{1}{3})^2 * (1 - \frac{1}{3})^{5-2}[/tex]
[tex]P(x = 2) = ^5C_2 * (\frac{1}{3})^2 * (\frac{2}{3})^{3}[/tex]
[tex]P(x = 2) = 10 * \frac{1}{9}* \frac{8}{27}[/tex]
[tex]P(x = 2) = \frac{80}{243}[/tex]
Apply the formula to the complete question
a 10 foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle betwween the top of the ladder and the wall changing when that angle is
Answer:
d∅/dt = √2/5 Rad/sec
Step-by-step explanation:
According to the Question,
Given That, a 10-foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle between the top of the ladder and the wall changing when that angle is π/4.Solution,
Let x be the Distance between the base of the wall and the bottom of the ladder.
and let ∅ be the angle between the top of the ladder and the wall.
Then, Sin∅ =x/10 so, x=sin∅ *10
Differentiating with respect to time t we get,
dx/dt = 10 * cos∅ * d∅ /dt
We have given that dx/dt = 2 ft/s and ∅ =π/4Now, Put these value we get
2 = 10 *(cos(π/4))* d∅/dt
2 = 10/√2 * d∅/dt
d∅/dt = √2/5 Rad/sec
What is the first step in solving the quadratic equation -5x^2+8=133?
taking the square root of both sides of the equation
subtracting 8 from both sides of the equation
squaring both sides of the equation
adding 8 to both sides of the equation
Answer:
Step-by-step explanation:
-5x²+8=133
-5x²=133-8
-5x²=125
x²=-25 ........... dividing 125 by -5
x=√-25..........Taking square root of -25
x=±5
Hope this might help you...
The first step in solving the quadratic equation -5x²+8=133 is subtracting 8 from both sides of the equation.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is -5x²+8=133
Minus five times of x square plus eight equal to one hundred thirty three.
x is the variable in the equation.
We have to solve for x
-5x²+8=133
The first step is to isolate the variable x to do this we have to subtract 8 from both sides
-5x² = 125
Divide both sides by 5
x² = -125/5
x² =-25
Hence, first step in solving the quadratic equation -5x²+8=133 is subtracting 8 from both sides of the equation.
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4a+b+16a^2-b^2 how to factorize this can u plz solve it
Answer:
(4a+b)(1+4a-b)
Step-by-step explanation:
4a+b+16a²-b²4a+b+(4a)²-(b)²4a+b+(4a+b)(4a-b)(4a+b)(1+4a-b)hope it helps
stay safe healthy and happy.Answer:
(4a + b)( 1 + 4a - b )
Step-by-step explanation:
4a + b + 16a² - b²
Step 1 :- Use a² - b² = ( a - b ) ( a + b ) to factor the expression.
4a + b + ( 4a - b ) ( 4a + b ).
Step 2 :- Factor out 4a + b from the expression.
(4a + b)( 1 + 4a - b )
A personal narrative essay is usually written in and in .
Answer:
in the first person participle.
Step-by-step explanation:
Complete the remainder of the table for the given function rule: y= x/4 + 7
Let's replace x with -4 and simplify
y = (x/4) + 7
y = (-4/4) + 7
y = -1 + 7
y = 6
This means x = -4 and y = 6 pair up together.
So 6 goes in the box under the -4
----------------------------------------------------------
Repeat those steps for x = 0
y = (x/4) + 7
y = (0/4) + 7
y = 0 + 7
y = 7
So 7 goes in the box under the 0
----------------------------------------------------------
Let's repeat those steps for x = 4
y = (x/4) + 7
y = (4/4) + 7
y = 1 + 7
y = 8
So 8 goes in the box under the 4
----------------------------------------------------------
Lastly, for x = 8, we get
y = (x/4) + 7
y = (8/4) + 7
y = 2 + 7
y = 9
9 goes in the box under the 8
----------------------------------------------------------
The y outputs we got were: 6, 7, 8, 9
Notice how each time y increases by 1, x goes up by 4.
This means slope = rise/run = 1/4
We can think of x/4 as (1/4)x to help see that the slope is 1/4.
A function assigns the values. The value of the y in the given table should be 6, 7, 8, and 9, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function of the x and y is given y=(x/4)+7, use this function to find the value of y for the given values of x. Thus,
x = -4
y = (-4/4)+7
y = -1+7
y = 6
x = 0
y = (0/4)+7
y = 7
x = 4
y = (4/4)+7
y = 8
x = 8
y=(8/4)+7
y = 9
Hence, the value of the y in the given table should be 6, 7, 8, and 9, respectively.
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There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is
7/12
There are 84 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answer:
49
Step-by-step explanation:
The probability of choosing a red marble is equal to the number of red marbles over the number of total marbles there are.
Therefore, let the number of red marbles be [tex]x[/tex].
We have the following equation:
[tex]\frac{x}{84}=\frac{7}{12}[/tex]
Cross-multiplying, we get:
[tex]12x=7\cdot 84,\\x=\frac{84\cdot 7}{12},\\x=\boxed{49}[/tex]
Therefore, there are 49 red marbles in the bag.
5 plus 6 times 8 plus 9 times 10 plus 8 plus 4 plus 2 plus 9 plus 8 plus 7 plus 5 plus 7 plus 6 times 7 times 9 times 8 times 5 times 4 times 3 times 2 times 1 times 6 times 8 times 9 times 12 times 17 times 19 times 20 times 12 times 11 times 13 times 14 times 15 times 16
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need ASAP.
Use point-slope form to write the equation of the line in slope-intercept form that passes through the points (0, -5) and (-3, 4).
Slope formula: m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction
Point-slope form: y – y1 = m(x – x1)
Slope-intercept form: y = mx + b
Choose the equation of the line.
y = –3x – 13
y = –3x – 5
y = –3x + 5
y = Negative one-third x + 13
Answer:
y = one-third x + 3
Step-by-step explanation:
use the order of operations -5 + 3(7.2 - 3.2)
Answer:
-5 + 3(7.2 - 3.2) equals 7.
Step-by-step explanation:
The order of operations states the order in which different mathematical operations should be done first, you can use the mnemonic PEMDAS to remember the order to complete each operation. PEMDAS states that the order must be followed as Parenthesis, Exponents, Multiplication/Division, and Addition/Subtraction. In the expression -5 + 3(7.2 - 3.2), the three mathematical operations being used are subtraction, multiplication, and parenthesis, so based on PEMDAS, the order to complete them is parenthesis, multiplication, and subtraction. -5 + 3(7.2 - 3.2) = -5 + 3(4) = -5 + 12 = 7, so that is your final answer.
[tex]\displaystyle\bf -5+3(7.2-3.2)=7\\\\1)\:7.2-3.2=4\\\\2)\:4\cdot3=12\\\\3)\:12-5=7[/tex]
Details
A movie theater has a seating capacity of 205. The theater charges $5.00 for
children, $7.00 for
students, and $12.00 of adults. There are half as many
adults as there are children. If the total ticket sales was $ 1482, How many
children, students, and adults attended?
Answer:
94 children, 64 students, and 47 adults attended the movie theater.
Step-by-step explanation:
Let; a be for adults, s for students, and c for children.
Make a system to solve for the amount of people.
c/a = 2
a + 2a + s = 205
3a + s = 205
Simplify.
s = 205 - 3a
s = 205 - 3a
c = 2a
Plug it in.
5c + 7s + 12a = 1482
10a + 7(205 -3a) + 12a = 1482
10a + 1435 - 21a + 12a = 1482
a + 1435 = 1482
a = 47
Substitute.
c = 2(47)
c = 94
Solve.
s = 205 - 3(47)
s = 64