let us build equation for unknown legs
If we keep the length pf one leg as x
the other leg would be x +3
so we can build a relationship using pythagoras theorem
x^2 + (x+3)^2 = 15^2
x^2 + x^2 + 6x + 9 = 225
2x^2 + 6x + 9 = 225
2x^2 + 6x+ 9-225 = 0
2x^2 + 6x - 216 = 0
x^2 + 3x - 108 = 0 dividing whole equation by 2
x^2 + 12x - 9x - 108 = 0
x ( x + 12 ) - 9 (x + 12) = 0
(x -9) ( x +12) = 0
solutions for x are
x = 9 or x = -12
as lengths cannot be negative
one side length is 9cm
and other which is( x + 3)
9 + 3
12cm
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:
Hypotenuse² = First Leg² + Second leg²
Let x represent the length of one leg. The other leg is three more = x + 3, hypotenuse = 15 ft. Hence:
15² = x² + (x + 3)²
x² + 6x + 9 + x² = 225
2x² + 6x - 216 = 0
x² + 3x - 108 = 0
x = - 12 or x = 9
Since the length cant the negative hence x= 9, x + 3 = 12
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
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What is the missing term in this arithmetic sequence? 9, 14, 19, __, 29, 34, …
Answer: 24 because you add 5 for every number ex: 9+5=14
Answer:
24
Step-by-step explanation:
The difference can be calculated by subtracting the second term with the first term.
d = 14 - 9
d = 5
The difference is 5.
Add 5 to 19.
19 + 5 = 24
A Canadian longitudinal study1 examined whether giving antibiotics in infancy increases the likelihood that the child will be overweight later in life. The study included children and found that of the children had received antibiotics during the first year of life. Test to see if this provides evidence that more than of Canadian children receive antibiotics during the first year of life. Show all details of the hypothesis test, including hypotheses, the standardized test statistic, the -value, the generic conclusion using a significance level, and a conclusion in context.
1. Clearly state the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. What is the conclusion?
4. Do we have evidence to conclude that more than 70% of Canadian infants receive antibiotics?
A. Yes
B. No
Answer:
1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70
2. Test Statistic : 0.54 , P value : 0.2946
3. Fail to reject null Hypothesis
4. No.
Step-by-step explanation:
1. Null hypothesis is 70% of children receive antibiotics.
Alternative hypothesis is more than 70% of children receive antibiotics.
2. Test statistic is calculated as;
z = [tex]\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }[/tex]
z = [tex]\frac{0.01}{0.0185}[/tex]
z = 0.54
3. p value is calculated as;
1 - right tailed probability
1 - 0.7054 = 0.2946
Determine whether the outcome of the following hypothesis test was a correct decision, a type I error, or a type II error. Claim: "Less than 40% of college students graduate with student loan debt." A hypothesis test of this claim resulted in the decision to reject H0. The actual percentage of college graduates with student loan debt is 45%.
Answer:
Step-by-step explanation:
The claim: "Less than 40% of college students graduate with student loan debt."
The null hypothesis: more than 40% of college students graduate with student loan debt." p >= 40%
If the actual percentage of college graduates with student loan debt is 45%. The researcher was supposed to fail to reject the null but since he rejected it when it was actually true, it is a type I error.
A type I error occurs when the research rejects the null when it is actually true.
What rule (i.e. R1, R2, R3, R4, or R5) would you use for the hawk and for the grizzly bear? a. R2 and R5 b. R1 and R3 c. None of the above d. R1 and R4
Answer:
I NEED POINTS
Step-by-step explanation:
Probability of landing on even # on a spinner; probability of rolling an odd # on a die
Answer:
Spinner: 50%
Die: 50%
Step-by-step explanation:
Well for the spinner it depends on the amount of numbers it has,
in this case we’ll use 6.
So The probability of landing on the even numbers in a 6 numbered spinner.
2, 4, 6
3/6
50%
Your average die has 6 sides so the odd numbers are,
1, 3, 5
3/6
50%
Help ASAP!!!!
Solve for X. Round to the nearest hundredth if necessary.
Answer:
11.47Step-by-step explanation:
Given : A right triangle
To do : Solve for x
Solution,
[tex]cos \: 55 = \frac{x}{20} [/tex] ( by definition of cos function, adjacent / hypotenuse )
[tex]0.5736 = \frac{x}{20} [/tex]
multiply both sides of the equation by 20
[tex](0.5736) \times 20 = x[/tex]
Calculate the product
[tex]11.471 = x[/tex]
Swipe both sides of the equation
[tex]x = 11.471[/tex]
Round answer to nearest hundredth
[tex]x = 11.47[/tex]
Hope this helps...
Best regards!!
Lines $y=(3a+2)x-2$ and $2y=(a-4)x+2$ are parallel. What is the value of $a$?
Answer:
-8/5Step-by-step explanation:
Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same
Let's get the slope of both equation. For the first equation;
y=(3a+2)x-2
We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2
Similarly for the second line;
2y=(a-4)x+2
Re-writing in the standard format we will have;
y = (a-4)x/2+2/2
y = (a-4)x/2 + 1
The slope of the second line is (a-4)/2
On equating the slope of both lines to get the value of 'a' we will have;
3a+2 = (a-4)/2
Cross multiplying
2(3a+2) = a-4
6a+4 = a-4
Collecting like terms;
6a-a = -4-4
5a = -8
a = -8/5
Hence the value of a is -8/5
determining the probability of events. please help :)
Answer:
C. 1/8
Step-by-step explanation:
Probability of shooting a goal on a throw is 2/4 = 1/2.
Probability of 3 in a row is (1/2)³ = 1/8.
01:
Which expression can be used to model the phrase the sum of three and a number?
Answer:
3+x
Step-by-step explanation:
sum= addition
a number= a number
Answer:
3+x
eplanation
Identify the percent, amount, and base in this problem What is 15% of 60?
Answer:
9
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
write the equation for taking away 5 from x gives 10
Answer:
[tex]\boxed{\sf x - 5 = 10}[/tex]
Step-by-step explanation:
Taking away 5 from x ⇒ subtracting 5 from x
[tex]\large {\sf x - 5[/tex]
Gives 10 ⇒ result is 10
[tex]\large {\sf x - 5 = 10[/tex]
what is 1.8÷0.004? using long division
Answer:
Hi! Answer will be below.
Step-by-step explanation:
The answer is 450.
If you divide 1.8 and 0.004 the answer you should get is 450.
Below I attached a picture of how to do long division...the picture is an example.
Hope this helps!:)
⭐️Have a wonderful day!⭐️
.If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3; however, if '
you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4. For what fraction is this true?
Answer:
The fraction that this is true for = 7/13
Step-by-step explanation:
From the above question
Let the numerator be represented by a
Let the denominator be represented by b
If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3
This means:
a + 5/b + 5 = 2/3
Cross Multiply
3(a + 5) = 2(b + 5)
3a + 15 = 2b + 10
Collect like terms
3a - 2b = 10 - 15
3a - 2b = -5..........Equation 1
If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4
This means:
a - 5/b - 5 = 1/4
Cross Multiply
4(a - 5) = 1(b - 5)
4a - 20 = b - 5
Collect like terms
4a - b = 20 - 5
4a - b = 15..........Equation 2
b = 4a - 15
3a - 2b = -5..........Equation 1
4a - b = 15..........Equation 2
Substitute 4a - 15 for b in equation 1
3a - 2b = -5..........Equation 1
3a - 2(4a - 15) = -5
3a - 8a + 30 = -5
Collect like terms
3a - 8a = -5 - 30
-5a = -35
a = -35/-5
a = 7
Therefore, the numerator of the fraction = 7
Substitute 7 for a in Equation 2
4a - b = 15..........Equation 2
4 × 7 - b = 15
28 - b =15
28 - 15 = b
b = 13
The denominator = b is 13.
Therefore,the fraction which this is true for = 7/13
To confirm
a) If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3
This means:
a + 5/b + 5 = 2/3
7 + 5/ 13 + 5 = 2/3
12/18 = 2/3
Divide numerator and denominator by of the left hand side by 6
12÷ 6/ 18 ÷ 6 = 2/3
2/3 =2/3
If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4
This means:
a - 5/b - 5 = 1/4
7 - 5/13 - 5 = 1/4
2/8 = 1/4
Divide the numerator and denominator of the left hand side by 2
2÷2/8 ÷ 2 = 1/4
1/4 = 1/4
From the above confirmation, the fraction that this is true for is 7/13
A simple random sample of 20 third-grade children from a certain school district is selected, and each is given a test to measure his/her reading ability. You are interested in calculating a 95% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points. What is the margin of error associated with the confidence interval
Answer:
Margin of Error = ME =± 5.2592
Step-by-step explanation:
In the given question n= 20 < 30
Then according to the central limit theorem z test will be applied in which the standard error will be σ/√n.
Sample Mean = μ = 64
Standard Deviation= S= σ = 12
Confidence Interval = 95 %
α= 0.05
Critical Value for two tailed test for ∝= 0.05 = ±1.96
Margin of Error = ME = Standard Error *Critical Value
ME = 12/√20( ±1.96)=
ME = 2.6833*( ±1.96)= ± 5.2592
The standard error for this test is σ/√n
=12/√20
=2.6833
HEREEEEEEEEEEEEEElollll
Answer:
Hey there!
Your answer would be 4/50. The total times she drawed a purple tile was 4, and she drawed 50 times.
Hope this helps :)
Which equation represents a population of 250 animals that decreases at an annual rate of 21%
Answer:
y= 250( 1-0.21)^x
Step-by-step explanation:
This represents exponential decay
The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
What is an exponential function?The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
It is given that a population of 250 animals is decreasing at an annual rate of 21%.
p = a x b[tex].^t[/tex]
p = a x (1+r)[tex].^t[/tex]
p = 250 x (1+(-0.21))[tex].^t[/tex]
p = 250(0.79)[tex].^t[/tex]
Note that r = -0.21 is negative to indicate we have exponential decay.
Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
To know more about exponential functions follow
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Please answer this correctly without making mistakes Please simplify the correct answer
Answer:
1/5 are towboats
Step-by-step explanation:
In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together
30k + 10k + 10k= 50k
In total there are 50,000 flag vessels
Of those 50,000, 10,000 of them are tow boats
10,000/50,000 can be simplified to 1/5
1/5 are towboats
Answer:
1/5
Step-by-step explanation:
Well to find the fraction we first need to know the total amount of Flag Vessels.
30,000 + 10,000 + 10,000 = 50,000
If there are 10,000 towboats we can make the following fraction.
10,000/50,000
Simplified
1/5
Thus,
the answer is 1/5.
Hope this helps :)
express 11011 in base two
Answer:
27
Step-by-step explanation:
Hello,
11011 in base 2 is
1 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 1 in base 10
which is 16 +8+2+1=27
Do not hesitate if you have any question
select the fraction equivalent of 0.06. reduce to the lowest terms
Answer: 3/50
Step-by-step explanation:
0.06 = 6/100 , 100 would be the denominator because we have two figures after the decimal point. Each figures can also be represented by 10,
Again,
0.06 = 6 × 10-²
Now 0.06 = 6/100
= 3/50.
Therefore, the fractional form = 3/50 in its lowest term.
In a random sample of 400 residents of Boston, 320 residents indicated that they voted for Obama in the last presidential election. Develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
Answer:
C.I = 0.7608 ≤ p ≤ 0.8392
Step-by-step explanation:
Given that:
Let consider a random sample n = 400 candidates where 320 residents indicated that they voted for Obama
probability [tex]\hat p = \dfrac{320}{400}[/tex]
= 0.8
Level of significance ∝ = 100 -95%
= 5%
= 0.05
The objective is to develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
The confidence internal can be computed as:
[tex]=\hat p \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }[/tex]
where;
[tex]Z_{0.05/2}[/tex] = [tex]Z_{0.025}[/tex] = 1.960
SO;
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{4 \times 10^{-4}}[/tex]
[tex]=0.8 \pm 1.960 \times 0.02}[/tex]
[tex]=0.8 \pm 0.0392[/tex]
= 0.8 - 0.0392 OR 0.8 + 0.0392
= 0.7608 OR 0.8392
Thus; C.I = 0.7608 ≤ p ≤ 0.8392
A necklace was on sale for 20% discount off the original price of
$1250.00. What was the final sale price if 12.5% VAT has to be
paid?
Answer:
= $ [tex] \mathsf{1125}[/tex]Step-by-step explanation:
[tex] \mathrm{Given}[/tex],
[tex] \mathrm{Discount\% = 20\%}[/tex]
[tex] \mathrm{Marked \: price = 1250}[/tex]
[tex] \mathrm{Now \: let's \: find \: the \: discount \: amount}[/tex]
[tex] \mathrm{discount \: amount = dis\% \: of \: MP}[/tex]
[tex] \mathrm { = 20\% \: of \: 1250}[/tex]
[tex] \mathrm{ = 250}[/tex]
[tex] \mathrm{let's \: find \: the \: selling \: price}[/tex]
[tex] \mathrm{ = MP \: - \: discount \: amount}[/tex]
[tex] \mathrm{ = 1250 - 250}[/tex]
= $ [tex] \mathrm{1000}[/tex]
[tex] \mathrm{lets \: find \: the \: Vat \: amount}[/tex]
[tex] \mathrm{vat \: amount = vat\% \: of \: sp}[/tex]
[tex] \mathrm{ = 12.5\% \: of \: 1000}[/tex]
= $ [tex] \mathrm{ 125}[/tex]
[tex] \mathrm{Now \: finally \: let's \: find \: the \: selling \: price \: with \: vat}[/tex]
[tex] \mathrm{selling \: price \: + \: vat \: amount}[/tex]
[tex] \mathrm{ = 1000 + 125}[/tex]
= $ [tex] \mathrm{1125}[/tex]
Therefore, The final sale of the necklace is $ 1125
Hope I helped
Best regards!
What additional information do you need to prove △ABC ≅ △DEF by the SSS Postulate? A. BC = EF B. AB = DE C. AC = DF
Answer:
AC = DF
Step-by-step explanation:
The SSS Postulate occurs when all three corresponding pairs of sides are congruent, therefore, the only missing pair is AC = DF.
What is 3/4 improper or proper or mixed
Answer:
proper because the numerator is lower than the denominator
What are the dimensions of the rectangle? PLEASE HELP!!
Answer:
2(x^2 + 8x -55)
Step-by-step explanation:
Well to do the box method we first need to simplify the given equation further to,
[tex]2x^2 + 16x - 110\\[/tex],
For this quadratic the box method doesn't work so we can divide everything by 2 make make it
2(x^2 + 8x -55)
Thus,
[tex]2x^2 + 16x - 110\\[/tex] factored is 2(x^2 + 8x -55).
Hope this helps :)
easy math please help!
Answer:
[tex]\boxed{ \sf 41.81}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(?)=\frac{2}{3}[/tex]
[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]
[tex]\sf ?= 41.81031489...[/tex]
Answer:
[tex]\boxed{41.81}[/tex]
Step-by-step explanation:
∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.
The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).
However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.
Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.
What scenario depicts two independent events
Step-by-step explanation:
A t
eacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students. The girls’ basketball team is playing against the boys’ basketball team. The coach chooses a captain for the girls’ team and then chooses a captain for the boys’ team. Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another. Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings.
Answer:
A.The school play opens tonight and it is raining.
B.Neva is hungry and she buys a snack from the concession stand.
C. Ari chooses a partner for a group project and then Ezekial chooses a partner from the remaining classmates.
D.Luka paints during school and he stains his shirt.
The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. _______________
b. Determine the installment price.b. _________________
c. Determine the finance charge.c. _________________
Answer:
see details below
Step-by-step explanation:
The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. ___$23450____________
29450 - 6000 = 23450
b. Determine the installment price.b. ___$792,22______________
"monthly payment of $792.22"
c. Determine the finance charge.c. __$5069.92_______________
A = 792.22
n = 36
finance charge = total paid - amount to be financed
= 36*792.22 - 23450
= 5069.92
M angle D=? What is the degree of the angle?
Answer:
80°Step-by-step explanation:
In ACB and ECD
AC =~ CE [ Given ]
BC =~ CD [ Given ]
<ACD =~ <ECD [ Vertical angles ]
Hence, ∆ ACB =~ ECD by SAS congruency of triangles.
Then, <B = <D
In ∆ABC , sum of all three angles must be 180°
<A + <B + <C = 180°
plug the values
[tex] 30 + < d \: + 70 = 180[/tex]
Add the numbers
[tex]100 + < d = 180[/tex]
Move constant to R.H.S and change it's sign
[tex] < d = 180 - 110[/tex]
Subtract the numbers
[tex] < d = 80[/tex] °
Hope this helps..
Best regards!!
The mean rate for cable with Internet from a sample of households was $106.50 per month with a standard deviation of $3.85 per month. Assuming the data set has a normal distribution, estimate the percent of households with rates from $100 to $115.
Answer:
The percent of households with rates from $100 to $115. is [tex]P(100 < x < 115) =[/tex]94.1%
Step-by-step explanation:
From the question we are told that
The mean rate is [tex]\mu =[/tex]$ 106.50 per month
The standard deviation is [tex]\sigma =[/tex]$3.85
Let the lower rate be [tex]a =[/tex]$100
Let the higher rate be [tex]b =[/tex]$ 115
Assumed from the question that the data set is normally
The estimate of the percent of households with rates from $100 to $115. is mathematically represented as
[tex]P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ][/tex]
here x is a random value rate which lies between the higher rate and the lower rate so
[tex]P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ][/tex]
[tex]P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ][/tex]
Where
[tex]z = \frac{x- \mu}{\sigma}[/tex]
Where z is the standardized value of x
So
[tex]P(100 < x < 115) = P[ -1.688< z < 2.208 ][/tex]
[tex]P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )[/tex]
Now from the z table we obtain that
[tex]P(100 < x < 115) = 0.9864 - 0.0455[/tex]
[tex]P(100 < x < 115) = 0.941[/tex]
[tex]P(100 < x < 115) =[/tex]94.1%
x varies directly as y, when x=4,y=3. find Y when x=5
Answer:
Y =4
Step-by-step explanation:
Hope it helps