Given:
[tex]\sqrt{18}[/tex]To find:
The root of 18 without using a calculator
There is a formula that gives an approximation of a square root without a calculator. This is given as:
[tex]\begin{gathered} \sqrt{N}\text{ = }\frac{N\text{ + M}}{2\sqrt{M}} \\ where\text{ N = is the number we want to find its root} \\ M\text{ = is a perfect square close the number we are to find} \\ That\text{ is a number we can find its root } \end{gathered}[/tex][tex]\begin{gathered} \text{N = 18} \\ M\text{ = 16 is the closest number to 18 we can find its root} \\ \\ substitute\text{ the values into the formula:} \\ \sqrt{18}\text{ = }\frac{18\text{ + 16}}{2\times\sqrt{16}} \\ \\ \sqrt{18}\text{ = }\frac{34}{2(4)} \end{gathered}[/tex][tex]\begin{gathered} \sqrt{18}\text{ = }\frac{34}{8} \\ \\ \sqrt{18}\text{ = 4.25} \end{gathered}[/tex]Verify the identity:
cos(x)+sin(x)/ sin(x) =1+cot(x)
From cosecant identity the expression cos(x)+sin(x)/ sin(x) =1+cot(x) was verified.
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) , where:
sin (x) = [tex]\frac{opposite\ leg}{hypotenuse}[/tex]
cos(x)=[tex]\frac{adjacent\ leg}{hypotenuse}[/tex]
tan (x) = [tex]\frac{\frac{opposite\ leg}{hypotenuse} }{\frac{adjacent\ leg}{hypotenuse} } = \frac{opposite\ leg}{adjacent\ leg}[/tex]
The question gives the following identity: [tex]\frac{cos (x)+sin(x)}{sin(x)}[/tex]
First, you should rewrite the identity using the cosecant identity - csc(x)= 1/sin(x) . Then,
(cos(x)+sin(x)) * csc(x)
After that, you should expand the previous expression.
cos(x)*csc(x) + sin(x) * csc(x)
cos(x)*1/sin(x) + sin(x) * 1/sin(x)
cos(x)/sin(x) + sin(x)/sin(x)
cot(x) + 1
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If I = prt, which equation is solved for t?
O 1-pr=t
O
1-P-1
I
pr
O 1+pr=t
The solution of the equation for t is t = i/pr
How to determine the equation for t?The equation is given as
i = prt
Divide both sides of the equation by p
So, we have the following equation
i/p = prt/p
Divide both sides of the equation by r
So, we have the following equation
i/pr = prt/pr
Evaluate the quotients
i/pr = t
Rewrite as
t = i/pr
By the above computation, we changed the subject of the formula in i = prt from i to t.
This implies that solving for t is a concept of subject of formula
Hence, the solution is t = i/pr
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Write the ratio statement as a fraction and reduced to the lowest term if possible
We must write the ratio 7 to 15 and reduce it to the lowest term if possible.
The ratio is:
[tex]\frac{7}{15}.[/tex]Because 15 is not divisible by 7, we conclude that the ratio is already in its lowest form.
Answer[tex]\frac{7}{15}[/tex]GET MARKED BRAINLIEST IF ANSWERED RIGHT, 30PTS
The probability that the customer came for lunch and did not order dessert is 7/113
The probability that the customer came for lunch or did not order dessert is 93/113
What is probability?It is the chance of an event to occur from a number of possible outcomes.
It is given by:
Probability = Number of required events / Total number of outcomes
We have,
Total number of customers = 113
Desert Non desert
Lunch 7 1 3
Dinner 30 63
The probability that the customer came for lunch and did not order dessert:
= 7 / 113
The probability that the customer came for lunch or did not order dessert:
= (7+13)/113 + (13 + 63)/113
= 20/113 + 73/113
= 93/113
Thus,
The probability that the customer came for lunch and did not order dessert is 7/113
The probability that the customer came for lunch or did not order dessert is 93/113
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The Beta club is selling chocolate to raise money for Beta convention. Chocolate bars sell for $1.25 each and chocolate covered almonds sell for $2.00 each. The Beta club needs to raise more than $375 for all members to attend the convention. The students can sell up to 500 bars and covered almonds altogether.
1. Write a system of inequalities that can be used to represent this situation.
2. The club sells 100 chocolate bars. What is the least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention? Justify your answer.
The system of inequalities is 1.25x + 2y >= 375 and x + y <= 500, while the smallest number of chocolate covered almonds is 400
The system of inequalitiesWe make use of the following representations:
x = chocolate bars
y = chocolate covered almond
Using the above as a guide, and the given parameters;
We have:
1.25x + 2y >= 375 -- the amount raised
x + y <= 500 --- number of bars sold
The least number of chocolate covered almonds that must be soldFrom the question, we have
x = 100
Substitute x = 100 in x + y <= 500
100 + y <= 500
Evaluate
y <= 400
So, the least amount to sell is 400
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solve this polynomial using factor by grouping x³+2x²+4x+8=0 show work
x³+2x²+4x+8=0
Rearrange
x³ + 4x + 2x²+ 8 = 0
x ( x² + 4 ) + 2( x² + 4) = 0
(x + 2) ( x² + 4) = 0
The factors are;
(x + 2) (x² + 4)
(x²+ 4) can further be simplified to give (x- 2i) (x + 2i)
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Karl spent $58.34 at the grocery store last week. This week he spent $72.78. How much more did he spend this week than last week on groceries?
(Type Answer)
He spent $14.44 more on groceries this week than last week
How to determine the additional amount that was spent this week?From the question, the given parameters are
Amount spent last week = $58.34
Amount spent this week = $72.78
The additional amount that was spent at the grocery store this week is calculated by subtracting the amount spent this week from the amount spent last week
This is represented as
Additional amount = Amount spent this week - Amount spent last week
Substitute the known values in the above equation
So, we have
Additional amount = 72.78 - 58.34
Evaluate the difference
Additional amount = 14.44
Hence, an additional of $14.44 was this week
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The ratio of the length of Skylar's bridge to the length of Karen's bridge is 3.4. Karen's bridge measure 48 inches.How long is Skylar's bridge
Answer:
These points are mine :)))
Step-by-step explanation:
Twelve less than seven times a number is sixteen. Find the number.
Answer:
4
Step-by-step explanation:
put in equation form
7x - 12 = 16
solve for x
7x = 28
x = 4
A simple random sample of 800 elements generates a sample proportion overline p =0.66 . ( Round your answers to four decimal places . ) ( a ) Provide a 90 % confidence interval for the population proportion . to ( b ) Provide a 95 % confidence interval for the population proportion . to
STEP - BY - STEP EXPLANATION
Whatto find?
• 90% confidence interval for the population proportion.
,• 95% confidence interval for the ppulation proportion.
Given:
n= 800
p=0.66
q=1- p= 1- 0.66 =0.34
a) Given a 90% confidence interval,
α =1- 0.90= 0.10
[tex]Z_{\frac{\alpha}{2}}=Z_{\frac{0.10}{2}}=Z_{0.05}=1.645[/tex][tex]C.I=\bar{P}\pm Z_{\frac{\alpha}{2}}\times\sqrt{\frac{\bar{P}\bar{q}}{n}}[/tex][tex]=0.66\pm1.645\times\sqrt{\frac{0.66\times0.34}{800}}[/tex][tex]\begin{gathered} =0.66\pm0.02755 \\ \\ =(0.6324,\text{ 0.6276\rparen} \end{gathered}[/tex]b)
Given 95% confidence interal.
1- 0.95 =0.
ANSWER
a) (0.6276, 0.6324)
i need help with this pls
The contrapositive of the statement is:
Jose isn't going for a bike ride if and only if he doesn't woke up early.
What is contrapositive?
A conditional statement's hypothesis and conclusion are switched, and both are then rejected, in a contrapositive. For instance, "if not B then not A" is the opposite of "if A then B." A conditional statement's contrapositive combines the inverse and converse.
The given statement is,
Jose wakes up early if and only if he is going for a bike ride.
We divide the statement into two parts.
1. Jose wakes up early.
2. He is going for a bike ride.
The negative of the statements are,
Jose doesn't wakes up early and he isn't going for a bike ride.
Therefore, the contrapositive of the statement is,
Jose isn't going for a bike ride if and only if he doesn't woke up early.
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Kaori is taking a free-throw.
H(d)H(d)H, left parenthesis, d, right parenthesis models the basketball's height (in meters) at a horizontal distance of ddd meters from Kaori.
What does the statement H(R)=4H(R)=4H, left parenthesis, R, right parenthesis, equals, 4 mean?
The height of the ball at a horizontal distance of R meters from Kaori is H(R)=4H.
Kaori taking a free throw is a guarantee. H(d) simulates the basketball's height (in meters) at d meters of horizontal separation from Kaori.
It is said that H(R) = 4H.
In this case, H(R) displays the height of a basketball instead of H(d). Therefore, it is evident that a basketball's height is 4H since H(R)=4H at d = R.
The horizontal distance from Kaori is R because d is the horizontal distance from Kaori.
Thus the height of the ball is 4H meters at a horizontal distance of R meters from Kaori, according to the expression H(R)=4H.
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Is ABC DEF? If so identify the similarity postulate or theorem that apples
ANSWER:
B. Similar - SAS
EXPLANATION:
Given:
Recall that the SAS Similarity Rule states that if two sides of one triangle are proportional to two corresponding sides of another triangle and the included angle in both triangles are congruent, then the two triangles are said to be similar.
Looking at triangles ABC and DEF, we can see that, we can see that;
[tex]\begin{gathered} \frac{AB}{DE}=\frac{BC}{EF} \\ \\ \frac{9}{3}=\frac{15}{5}=3 \end{gathered}[/tex][tex]\begin{gathered} m\angle B\cong m\angle E \\ 40^{\circ}\cong40^{\circ} \end{gathered}[/tex]Since the two corresponding sides of both triangles are in equal proportion and the included angle in both triangles are congruent, then triangles ABC and DEF are similar by the SAS Similarity Rule
What is the distance between the points (−3, −5) and (−3, −7)?
The distance between the points (−3, −5) and (−3, −7) is 2 units.
How to use distance formula?The distance formula gives the shortest distance between two points in a two-dimensional plane.
The distance formula is a useful tool for calculating the distance between two points.
Therefore,
d = √(x₂ - x₁)²+(y₂ - y₁)²
Let's find the distance between the points (−3, −5) and (−3, −7).
Hence,
x₁ = -3
x₂ = -3
y₁ = -5
y₂ = -7
d = √(-3 + 3)² + (-7 + 5)²
d = √(-2)²
d = √4
d = 2
Therefore, the distance between the point is 2 units.
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Scott paid $13.24 for a 3.41 pound bag of shrimp at one store. The following week, he paid $18.99 for a 4.96 pound bag at another store. Find the unit price for each bag. Then state which bag is better buy based off the unit price. Round your answers to the nearest cent.
Solution:
Scott paid;
$13.24 for 3.41-pound bag of shrimp
This means,
[tex]\begin{gathered} \text{ \$13.24=3.41pound} \\ 3.41\text{pound}=13.24 \\ \text{The unit price means the price of 1pound.} \\ 1\text{pound=}\frac{13.24}{3.41} \\ \text{Unit price= \$3.88 to the nearest tenth} \end{gathered}[/tex]$18.99 for 4.96-pound bag of shrimp
This means,
[tex]\begin{gathered} \text{ \$18.99=4.96pound} \\ 4.96\text{pound}=18.99 \\ \text{The unit price means the price of 1pound.} \\ 1\text{pound=}\frac{18.99}{4.96} \\ \text{Unit price= \$3.83 to the nearest tenth} \end{gathered}[/tex]Therefore, the bag that is a better buy based on the unit price is the 4.96-pound because of the unit price which is lesser than the unit price for the 3.41-pound bag.
Thus, the 4.96-pound is a better buy.
Type the correct answer in the box. The area of the figure is (BLANK) square units.
Given:
Find: Area of the figure.
Sol:
The area of Triangle ABH is:
Area
[tex]\text{ Area=}\frac{1}{2}\times\text{ Base}\times\text{ height}[/tex]In triangle is:
Base = (9-3)
Height = 8
So Area of ABH is:
[tex]\begin{gathered} \text{ Area=}\frac{1}{2}\times6\times8 \\ \\ =24 \end{gathered}[/tex]Area of rectangle BDFH so,
[tex]\text{ Area=Length}\times\text{ width}[/tex]Width = 8
[tex]undefined[/tex]Seven more than the product of 14 and Mabel's ageUse the variable m to represent Mabel's age.
7+14m
Explanation
Step 1
Let
m represents Marbel's age
Then,
the product of 14 and Mabel's age=
[tex](m\cdot14)=14[/tex]now, Seven more than the product of 14 and Mabel's age
then
[tex]7+(m\cdot14)=7+14m[/tex][tex] {3x}^{4} {y}^{ - 2} x {2x}^{ - 1} {y}^{2} [/tex]whats the answer
Multiply the numbers and combine exponents with the same base.
Juan is investing his money. He thinks that he should make $12 for every $100 he invests. How much does he expect to make in an investment of $4200?
We have to estimate how much he expects to make investing $4200 if he should make $12 for every $100.
We can apply the rule of three as:
[tex]\begin{gathered} 100-->12 \\ 4200-->x=4200*\frac{12}{100} \\ x=4200*0.12 \\ x=504 \end{gathered}[/tex]Answer: he expects to make $504.
Assume boat license plates have two numbers, followed by three letters, followed by two numbers. Letters and numbers can repeat multiple times in the same license plate. For example, possible license plates are 12ABC40 and 55EEE55. How many different license plates are possible?
Answer:
175,760,000
Step-by-step explanation:
This is the counting principle.
There are 7 positions. Multiply the number of possible characters in each position.
_ × _ × _ × _ × _ × _ × _
The numbers are from 0 to 9, so there are 10 of them.
There are 26 letters in the English alphabet.
10 × 10 × 26 × 26 × 26 × 10 × 10
Answer: 175,760,000
For what value of x is the parallelogram a rhombus?
The figure is a rhombus when x=?
The given parallelogram is a rhombus when x = 9 units
The parallelogram is a four sided plane with opposite sides parallel. So the opposite angles are equal. A parallelogram that has all angles are right angles is called rectangle.
The rhombus is a four sided plane with all of whose sides have the same length.
The sides are given,
9x-8 and 5x+28
In rhombus all the sides are equal
Then the equation will be
9x-8 = 5x+28
Rearrange the terms and solve it
9x-5x = 28+8
4x = 36
x = 36/4
x = 9
Hence, the given parallelogram is a rhombus when x = 9 units
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Solve for x log 3x+4) = 2
Step 1:
Write the equation
[tex]\log ^{3x+4}_4\text{ = 2}[/tex]Step 2:
Express the equation in exponential form
[tex]\begin{gathered} \log ^{3x+\text{ 4}}_4\text{ = 2} \\ 3x+4=4^2 \\ 3x\text{ + 4 = 16} \\ 3x\text{ = 16 - 4} \\ 3x\text{ = 12} \\ x\text{ = }\frac{12}{3} \\ x\text{ = 4} \end{gathered}[/tex]Final answer
x = 4
a skydiver jumps out of an airplane. after 0.8 seconds, she has fallen 100 feet.after 3.1 seconds,she has fallen 500 feet.Emtiaz says that the skydiver should fall about 187.5 feet in 1.5 seconds. is his answer reasonable?
Is his answer reasonable: No, Emtiaz's answer is not reasonable because he assumed that the rate of descent was proportional.
What is the average rate of change?The average rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
Next, we would determine the rate at which the skydiver falls per seconds:
Rate = time/distance
Rate = 100/0.8
Rate = 125
Also, an equation which models the height (h) of the skydiver at a 0.8 seconds is given by:
h = 125t
At 3.1 seconds, we have:
Rate = time/distance
Rate = 500/3.1
Rate = 161.3
At 1.5 seconds, we have:
Rate = time/distance
Rate = 187.5/1.5
Rate = 125
Therefore, the average rate of change at each time interval is not equal and as such Emtiaz's answer is not reasonable because the rate increases as the time increases.
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Which statement explains how you could use coordinate geometry to prove the diagonals of a quadrilateral are perpendicular?
To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.
What is coordinate geometry?
The science of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry).
Finding the difference between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
m=(rise/run) = (y2-y1)/(x2-x1)
(x1,y1) = coordinates of the line's first point
(x2,y2) = coordinates of the line's second point
To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.
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your dinner bill was $21.00 if you leave a 15% tip, how much will the tip be?
Solution:
Given:
The dinner bill = $21.00
The tip = 15% of the bill
Hence,
[tex]\begin{gathered} =15\text{ \% of \$21} \\ =\frac{15}{100}\times21 \\ =\frac{315}{100} \\ =\text{ \$3.15} \end{gathered}[/tex]Therefore, the tip will be $3.15
The heights of 8th grade boys are normally distributed with a mean of 50 inches and a standard deviation ofDraw and label a normal distribution curve below. 4 pts)2) pos) Approximately 99.7% of the heights fall betweenandb) pts) The middle 58% of heights fall betweenandps) What percentage of grade boys are between 55 and 50inches tall2 pts) What is the probability that an sgrade boy will beshorter than 55 inches
EXPLANATION
Let's see the facts:
Heights of 8th grade boys ---------------> Normally distributed
Mean= 50 inches
Standard deviation= 4 inches
d) Probability that boy shorter than 56 inches:
x=56
P(x<56)
We know that z-score=
[tex]z=\frac{x-\mu}{\sigma}[/tex]Replacing terms:
[tex]z=\frac{56-50}{4}=1.5[/tex]P-value from Z-table =
P(x<56) = 0.93319
Answer: The probability that an 8th grade boy will be shorter than 56 inches is 0.93319*100= 93.3%.
c) Percentage of 8th grade boys that are between 56 and and 60 inches tall is:
[tex]z-score_{56}=\frac{56-50}{4}=\frac{3}{2}[/tex]P-value from Z-table =
P(x<60) = 0.93319
[tex]z-score_{56}=\frac{60-50}{4}=\frac{5}{2}[/tex]P-value from Z-table =
P(x<60) = 0.99379
Then, subtracting both probabilities.
P(56
Answer: the percentage of 8th grade boys that are between 56 and 60 inches tall is 0.0606*100 = 6.06%.
a) We have that,
According to the Empirical Rule, we can assevere that 50+- 3σ = 50+- 3*4 ---->
50 + 12 = 62 inches
50 - 12 = 38 inches
About 99.7% of 8th grade boys height will fall between 38 inches and 62 inches.
Answer: Approximately 99.7% of the heights fall between 38 inches and 62 inches.
b) According to the Empirical Rule, we can assevere that around 68% of the data will fall within one standard deviation of the mean. As we already know, the standard deviation σ is a natural yardstick for any measurements that follow a normal distribution.
So, 50 +- σ = 50 +- 4 ---->
50 + σ = 50 + 4 = 54
50 - σ = 50 - 4 = 46
Answer: About 68% of 8th grade boys height will fall between 46 inches and 54 inches.
Lisa’s car gets 31 miles per gallon of gasoline. How many miles can she drive on 22 gallons of gas? Lisa can drive ____ miles.
Lisa's car gets 31 miles per gallon.
Thus in 22 gallons she can drive,
22x31=682 miles.
Lisa can drive 682 miles.
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x³ is N²/15. The index form of a number is that digit written as an exponential expression or an unmarried number presented to another number.
What is meant by index form?A number's index form is that number written as an exponential expression or as a single number raised to another number. The exponent, or index, of an exponential expression indicates how many times the base must be multiplied by itself to evaluate the expression.
This fact can be used to write a number in index form. An index number is a number that has been multiplied by a power. The power, also known as the index, indicates how many times the number must be multiplied by itself. For example, 25 means multiplying 2 by itself five times
= 222222 = 32. There are several important index number rules:
ya × yb = y.
Therefore,
[tex]$x^3=\frac{N^2}{15}[/tex]
For [tex]$x^3=f(a)$[/tex] the solutions are
[tex]$x=\sqrt[3]{f(a)}, \sqrt[3]{f(a)} \frac{-1-\sqrt{3} i}{2}, \sqrt[3]{f(a)} \frac{-1+\sqrt{3} i}{2}$$$[/tex]
[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2},[/tex][tex]$x=\sqrt[3]{\frac{N^2}{15}} \frac{-1-\sqrt{3} i}{2}$$[/tex]
Simplify
[tex]$\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2}: \quad-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]
[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}-\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]
[tex]$x^3=\frac{N^2}{15}[/tex]
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Solve this system of equations usingthe substitution method.y = x + 9y = - 4x – 6-
Given:
Here the system of eqution is given as
[tex]\begin{gathered} y=x+9 \\ y=-4x-6 \end{gathered}[/tex]Required:
Solve using the substitution method
Explanaton:
First put
[tex]y=x+9[/tex]in
[tex]y=-4x-6[/tex]we get
[tex]x+9=-4x-6[/tex]now isolate x
[tex]\begin{gathered} x+4x=-9-6 \\ 5x=-15 \\ x=-3 \end{gathered}[/tex]now put the value of x first equation
[tex]\begin{gathered} y=-3+9 \\ y=6 \end{gathered}[/tex]Final answer:
Solution of given system of equation by using elimination is
[tex]\begin{gathered} x=-3 \\ y=6 \end{gathered}[/tex]
A prospector graphed the locations of a gold vein and all of the gold dust strikes in the vicinity. He positioned the gold vein at ( − 8 , 9 ) ( - 8 , 9 ) and the farthest gold dust strike at ( 7 1 , 9 ) . ( 7 1 , 9 ) . If each unit on the graph represents 1 m i l e , then how far away from the gold vein is the farthest gold dust strike?
The actual distance between the golf vein and the farthest gold dust strike is; 79 miles.
What is the distance between the gold vein and the farthest gold dust strike?It follows from the task content that the actual distance between both locations is to be determined.
It follows from the distance formula in coordinates geometry that;
D = √{(x2 - x1)² + (y2 - y1)²}
Therefore, the distance between the gold vein and the farthest gold dust strike is;
D = √{(-9 -(-9))² + (71 - (-8))²}
D = √79²
D = 79.
Ultimately, the distance on the graph is 79 units and since each unit on the.graoh represents 1 mile, the actual distance between the gold vein and the farthest gold dust strike is; 79 miles.
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