The FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made.
So, we have the inequality: 3(n − 6) < 2(n + 12)
Now, verify the false inequality as follows:
(A) S:{−5}
3(n − 6) < 2(n + 12)
3(-5 − 6) < 2(-5 + 12)
3(-11) < 2(7)
-33 < 14: TRUE
(B) S:{3}
3(n − 6) < 2(n + 12)
3(3 − 6) < 2(3 + 12)
3(-3) < 2(15)
-9 < 30: TRUE
(C) S:{12}
3(n − 6) < 2(n + 12)
3(12 − 6) < 2(12 + 12)
3(6) < 2(24)
18 < 48: TRUE
(D) S:{42}
3(n − 6) < 2(n + 12)
3(42 − 6) < 2(42 + 12)
3(36) < 2(54)
108 + 108: FALSE
Therefore, the FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.
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Correct question:
Given the inequality 3(n − 6) < 2(n + 12), determine which integer makes the inequality false.
a. S:{−5}
b. S:{3}
c. S:{12}
d. S:{42}
Wrote an equation with a vertex : (4,-5)
passes through: (2,-1)
write the expression as a sum and/or difference of logarithms. express exponents as factors.log5 a3 b
Expression of logarithms is log₅a³b = 3log₅a + log₅b.
Given expression is log₅a³b.
We have to express given expression as a sum or difference of logarithms.
We know the logarithmic formulas which is,
logₐ(PQ) = logₐP + logₐQ
logₐ([tex]P^{Q}[/tex]) = QlogₐP
we will use above formulas and solve the given equation.
log₅a³b = log₅a³ + log₅b
log₅a³b = 3log₅a + log₅b
Logarithms, like exponents, have many helpful properties that can be used to simplify logarithmic expressions ans solve logarithmic equation.
The product property states that to miltiply two powers that have the same base, add the exponents.
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Use the grid to help you fill in the blank.
0.9 × ___ = 0.27
Answer:
0.3
Step-by-step explanation:
0.9 times 0.3 equals 0.27
$$1,2,2,4,8,32,256,\ldots,$$each term (starting from the third term) is the product of the two terms before it. for example, the seventh term is $256$, which is the product of the fifth term ($8$) and the sixth term ($32$). this sequence can be continued forever, though the numbers very quickly grow enormous! (for example, the $14^{\text{th}}$ term is close to some estimates of the number of particles in the observable universe.) what is the last digit of the $35^{\text{th}}$ term of the sequence?
The last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.
Given that,
Each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it. For instance, the seventh term, which is the sum of the fifth ($8) and sixth ($32) terms, is $256. Though the numbers very rapidly become large, this series can go on indefinitely! In terms of the number of particles in the observable universe, the $14 term, for instance, is close to some estimations.
We have to find what is the final digit of the sequence's $35 term.
We know that,
Remember the Fibonacci sequence, which goes 1, 1, 2, 3, 5, 8, 13, 21..., where each word is the total of the one before it. Continuing the above pattern, if Fn is the n-th Fibonacci number, we would arrive at
aₙ=a₂ˣₙ₋₁a₁ˣₙ₋₂=2ˣₙ₋₁
A periodic series of residues mod 10 is left behind by the sequence of positive powers of 2:
2≡2(mod 10)
2²≡4 (mod 10)
2³≡8 (mod 10)
2⁴≡16 (mod 10)
2⁵≡32 (mod 10)
2⁶≡64 (mod 10)
And so forth; this series of residues has a 4-year period.
The taken mod 4 period is 6:
34≡4 (mod 6)
F₃₄≡3 (mod6)
2³=8
So, the last digit of a₃₅ is 8.
Therefore, the last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.
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Colorful wool is being woven into a scarf in cold, damp Ireland. Wool is used for scarves, sweaters, hats, and gloves because it is a good insulator. If wool is a good insulator, what substance would be a good conductor?
A plastic
B fur
C cotton
D metal
Anyone know this? Kind of struggling.
Answer:
It's -5 + 3 basicaly because 2 negatives is one positive. So the answer is -2.
evaluate the summation for the indicated value of the variable. 1(1!) 2(2!) 3(3!) 4(4!) m(m!); m
The sum of the indicated variable is 23.
What is variable?
A variable is an alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables are specially employed in the case of pure mathematics expression or pure mathematics.
MAIN body:
the correct expression is as follows :
1(1!) +2(2!) +3(3!)+ 4(4!) ........+ m(m!) where m = 3
for m= 3
the expression becomes:
=1(1!) +2(2!) +3(3!)
factorial means we need to multiply the number until it reaches 1.
= 1*1 + 2*2*1 + 3*3*2*1
= 1+ 4+ 18
= 23
Hence the sum of expression is 23.
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6(x−2)=−18
due today
Answer: -1
Step-by-step explanation: 6x-12=-18
+12= +12
------------------
-6/6=-1
a keypad at the entrance of a building has 10 buttons labeled 0 through 9. what is the probability of a person correctly guessing 8 digit entry code
The probability is it that someone will correctly guess an 8-digit entry code is 0.022.
Given that,
A keypad with 10 buttons marked 0 through 9 is located at the building's entrance.
We have to find how much probability is it that someone will correctly guess an 8-digit entry code.
We know that,
Probability is defined as the ratio of the number of required outcomes to the total number of outcomes.
Based on the details provided;
One outcome is expected if the needed number of outcomes is 8-digits.
Since there are 10 numbers and 8 numbers need to be chosen, the total number of outcomes is ¹⁰C₈.
Considering that the lock can only be opened by 8 digits;
The probability that someone will properly guess a 8-digit input code is
P=1/¹⁰C₈
P=1/10!/8!2!
P=1/10×9/2
P=1/45
P=0.022
Therefore, The probability is it that someone will correctly guess an 8-digit entry code is 0.022.
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What is the value of x?
Answer: 2
Step-by-step explanation:
Since both triangles are similar you can set both side lengths to be equal
4x = 16x -24
Isolate x on one side
-12x = -24
Then solve for x
x = 2
If line segment AB represents 50%, what is the length of a line segment that is 100%?
Answer:
it would be CD or 50%
Step-by-step explanation:
if a cup of diced cucumbers weighs 5.3 ounces, how many pounds of prepped cucumbers will you need for your 140 house salads?
46 pounds of prepped cucumbers are needed for 140 house salads.
It is given that one cup of diced cucumbers weighs 5.3 ounces.
Also, we know that one pound= 16 ounces or 1-ounce measure 1/16 pounds, we can do it in any way.
Thus, firstly, we will convert the ounces into pounds.
thus, 5.3 ounces= 5.3/16 pounds
Now, we need prepped cucumbers for 140 house salads, According to the given question.
thus, pounds needed for 140 house salads= 5.3/16*140
=> 46 pounds (nearly)
Thus, 140 house salads need nearly 46 pounds of cucumbers.
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4. Identify each of the following polygons:
Answer:
Step-by-step explanation:
1. Square
2. Rhombus
3. Trapezoid
4. Diamond
5. Octogon
6. Triangle
7. Pentagon
8. Hexagon
9. Triangle?
Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence increases the margin of error will and the confidence interval will be A larger sample size will improve the accuracy of the confidence interval, therefore margin of error will and the confidence interval will be A) Decrease, wider. Increase, narrower B) Decrease, narrower. Increase, wider C) Increase, wider. Decrease, narrower. D) Increase, narrower. Decrease, wider.
Option-C is correct that is increase, wider. If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.
Given that,
By completing the blanks, the sentence is complete. When generating a confidence interval, the margin of error and the confidence interval will be larger if the level of confidence grows.
We have to find the accuracy of the confidence interval will increase with a larger sample size, so the margin of error and the confidence interval will be-----.
We know that,
If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.
The margin of error is a phrase that conveys how much sampling error there is in the data that was gathered or in the parameter estimates. Accordingly, the credibility of the poll will decrease as the margin of error increases. It displays the degree of estimation accuracy.
Three things determine the margin of error:
Confidence level: The margin of error grows in proportion to the level of confidence.
Sample size: The margin of error gets smaller as the size of the random sample gets bigger.
Population standard deviation: The population's standard deviation is: For a given level of confidence, our interval will be wider the more dispersed the population is.
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if you can notice the difference between 10- and 11-pound weights, which of the following weights could you differentiate from a 100-pound weight?
If we can notice the difference between 10- and 11-pound weight, we can differentiate 110-pound weight from a 100-pound weight.
What is weight?All things close to Earth are constantly subject to the force known as weight. All items are pulled downward toward the Earth's core by the gravity of the planet. On the other hand, weight is a measurement of how much gravity pulls an item downward. The mass of the thing has an impact on this force; the heavier the object, the stronger gravity's pull is. The force of gravity acting on a body is the most typical definition of weight given in introductory physics textbooks. This is sometimes formulated as W = mg, where W is the weight, m is the object's mass, and g is the acceleration due to gravity.
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If the nth term of a number sequence is n^2 + 2n,
find the first 3 terms and the 10th term.
Answer:
3, 8, 15 and 120
Step-by-step explanation:
to find the first 3 terms, substitute n = 1, 2, 3 into the nth term rule
n = 1 : 1² + 2(1) = 1 + 2 = 3
n = 2 : 2² + 2(2) = 4 + 4 = 8
n = 3 : 3² + 2(3) = 9 + 6 = 15
the first 3 terms are 3, 8, 15
to find the 10th term , substitute n = 10 into the rule
n = 10 : 10² + 2(10) = 100 + 20 = 120
if the original recipe calls for 50 portions, 6oz each and the new recipe calls for 100 portions at 5oz each, what is the recipe conversion factor?
By using multiplication and division of integers, it can be calculated that
Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6
What is multiplication and division of integers?
At first it is important to know about integers
Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem where multiplication and division of integers is required
The original recipe calls for 50 portions, 6oz each
Required yield of the original recipe = 50 [tex]\times[/tex] 6 = 300 oz
The new recipe calls for 100 portions at 5oz each
Required yield of the new recipe = 100 [tex]\times[/tex] 5 = 500 oz
Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6
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Write an equation for the line parallel to the given line that contains C.
C(1,5); y= -4x+7
Answer:
y=-4x+9
Step-by-step explanation:
We will find an equation in the form of y = mx + b. We know m must be -4(because the slope must be the same for parallel lines), so we need to solve for b, which is the y-intercept. To do that, we will plug in the point C, giving us [tex]5 = -4 * 1 + b[/tex]. Adding 4 to both sides gives us b = 9, so that is the y-intercept.
Write an equation of a line in slope intercept form with a slope of 3/2 that passes through point (4,7).
Answer:
y
=
−
3
2
x
+
13
Explanation:
First write it using point-slope form:
y
−
7
=
−
3
2
(
x
−
4
)
Now simplify to slope-intercept:
Add 7 to each side:
y
=
−
3
2
(
x
−
4
)
+
7
Distribute
−
3
2
to each term in the parentheses:
y
=
−
3
2
x
+
6
+
7
y
=
−
3
2
x
+
13
hope I helped you:)
Which additional piece of information would show that quadrilateral WXYZ is a rhombus?
The additional piece of information that is needed to show that the quadrilateral is a rhombus is given as follows:
The angle measures.
What is a rhombus?A rhombus is a quadrilateral, and is a special case of a parallelogram.
For the parallelogram to represent a rhombus, these following conditions need to be respected:
Parallelism of opposite sides.Congruence of opposite angles -> Same measures.All the sides are equal in length.The bisection of diagonals happen at right angles.To verify if two sides are parallel, we need to verify their slopes, which are dependent on their angle measures. Hence these angle measures are the missing piece of information to define if the quadrilateral is a rhombus.
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(2+8) + 10 ^2 +60 divided 10
Answer: 17
Step-by-step explanation:
Answer:
Step-by-step explanation:
116
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
If y = 21 when x = 14, find y when x = 40 .
ur answer should have ,60
Answer:
see explanation
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 21 when x = 14 , then
21 = 14k ( divide both sides by 14 )
[tex]\frac{21}{14}[/tex] = k , that is
k = [tex]\frac{3}{2}[/tex] = 1.5
y = 1.5x ← equation of variation
when x = 40 , then
y = 1.5 × 40 = 60
in a regression analysis, a(n) is used to predict a(n) . a. ordinal variable, ratio variable b. independent variable, dependent variable c. nominal variable, independent variable d. response variable, explanatory variable
In a regression analysis, a(n) is used to predict a(n) is known as option (b).independent variable, dependent variable.
Regression analysis:
In the concept of statistics, the regression analysis is useful to come up with a predictive model consisting of dependent and independent variables. And the R-squared value for a regression equation indicates the percentage of variability in the dependent variable being expressed by the variability in the independent variables.
Given,
Here we need to find the type of variable for a regression analysis, a(n) is used to predict a(n).
As per the definition of regression analysis, in the given question, we have two variable there are
=> a(n)
After prediction, the predicted value of a(n).
Here the first one is the independent variable because the this value is the based to predict the value of the other one is the dependent variable.
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Victoria deposited $15,000 into a savings account that earns an annual simple interest rate of 0.2% to the nearest 10th of a year how long will it take for the account to reach 15,500
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
sus
It will take about 16.7 years to reach $15500.
What is the interest rate?The percentage that a lender adds to the amount of money lent to them is called an interest rate.
Given that, the initial deposited amount is P = $15000, the interest rate is r= 0.2% annually, and the final amount is $15500.
The interest earned is calculated by subtracting the initial amount from the final amount:
15500-15000
=500
Therefore, the interest earned is $500.
Now, the formula for the simple interest is:
interest = P × r × t
Substitute the known values:
500 = 15000 × 0.2% × t
500 = 15000 × 0.2/100 ×t
500 = 30t
t = 500/30
t = 16.7
Hence, It will take about 16.7 years to reach $15500.
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One angle of a triangle measures 75°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
well, since a triangle has a total of 180° interior angles, that means 180 - 75 = 105 is leftover for the other two remaining angles.
now, they're in a 2 : 5 ratio, well, let's simply divide 105° by (2 + 5) and distribute accordingly.
[tex]2~~ : ~~5\implies 2\cdot \frac{105}{2+5}~~ : ~~5\cdot \frac{105}{2+5}\implies 2\cdot 15~~ : ~~5\cdot 15\implies \text{\LARGE 30~~ : ~~75 }[/tex]
the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km. what is the difference between these distances?
HELPPPPPPPPPPPP ASAP!!!!
The difference between these distances on the Earth is 3.32 × 10⁴.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.
The difference will be:
= 4.00x10^4 km - 6.8x10^3 km.
= 3.32 × 10⁴
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A given triangle has vertices at (-3,1) (2,4) and (5,-3) . If the triangle were rotated 180 degrees counterclockwise, the new coordinates would be ?
The new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4), (-5, 3).
Define transformations.A function, f, that maps to itself are known as a transformation, or f: X → X. The transformation results in the pre-image X becoming the picture X. This transformation can utilize any operation, or a combination of operations, including translation, rotation, reflection, and dilation.
Given, the triangle vertices (-3, 1) (2, 4), and (5, -3).
When the triangle turned 180 degrees counterclockwise, we must determine the new coordinates;
When we rotate 180 degree counterclockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
Therefore, the new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4), (-5, 3).
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Nancy i making acceorie for the occer team. She ue 566. 28 inche of fabric on headband for 36 player and 3 coache. She alo ue 306. 36 inche of fabric on writband for jut the player. How much fabric wa ued on a headband and writband for each player?
Using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.
So, given that we've done it:
There are 35 players.
There are two coaches.
The cloth on the headbands measures 598.66 inches in length.
Just for the players, the wristbands include 302.05 inches of fabric.
Each player's headband's fabric length is specified by:
= Total inches/Total number of persons
= 598.66/37
= 16.18 inches
Each player's wristband's fabric length is specified by:
= Total inches/Number of persons
= 302.05/35
= 8.63 inches
Therefore, using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.
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Complete question:
Nancy is making accessories for the soccer team. She uses 598.66 inches of fabric on headbands for 35 players and 2 coaches. She also uses 302.05 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
f(x) = 2x²+ 3x - 14.
Answer:
Step-by-step explanation:
domain = all real numbers
range = {-121/8,∞)x-intercepts (2,0)
y-intercepts (0,-14)
vertex = minimum (-3/1 - 121/8)
Answer: Okay so I got,
1) x intercept = (2, 0), (-7/2, 0) and y intercept (0, -14)
2) 'x' equals to..
-Exact Form: 2, -7/2
-Decimal Form: 2, -3.5
Hope this helps!
suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. random samples of batteries are taken for each brand and the following data are recorded: sample 1: n1
The test statistic of two brands of batteries is -2.177.
How to calculate test statistic?[tex]n_1[/tex] = size of sample 1 = 16
[tex]n_2[/tex] = size of sample 2 = 21
[tex]\bar{x_1}[/tex] = mean of sample 1 = 210
[tex]\bar{x_2}[/tex] = mean of sample 2 = 225
[tex]\sigma_{1}[/tex] = standard deviation of sample 1 = 20
[tex]\sigma_{2}[/tex] = standard deviation of sample 2 = 23
T test is test for statistical hypothesis that follows t-distribution table under null hypothesis. T test is used when test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. So, for this case we use t test for test statistic,
t = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}}[/tex]
t = [tex]\frac{210-225}{\sqrt{\frac{20^2}{16}+\frac{23^2}{21}}}[/tex]
t = [tex]\frac{-15}{\sqrt{\frac{400}{16}+\frac{529}{21}}}[/tex]
t = -15 / 7.0845
t = -2.117
Thus, the two brands of batteries have test statistic result is -2.117
Your question is incomplete, but most probably your full question was
Suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. Random samples of batteries are taken for each brand and the following data are recorded:
Sample 1: n1= 16, X1 = 210, s1= 20
Sample 2: n2= 21, X2 = 225, s2= 23
What is the test statistic assuming unequal population standard deviations?
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