Is the following figure a parallelogram? Why?

A sample of 300 urban adult residents of a particular state revealed 65 who favored increasing the highway speed limit from 55 t

forsale [732]

Answer and explanation:

Null hypothesis(H0) says sentiment for increasing speed limit in the two populations is the same

Alternative hypothesis(Ha) says sentiment for increasing speed limit in the two populations is different

Where p1 is the first population proportion =65/297= 0.22

And p2 is the second population proportion = 78/189= 0.41

P= p1+p2/n1+n2= 65+78/297+189= 0.29

Hence H0= p1-p2=0

Ha=p1-p2≠0

Test statistic= p1-p2/√p(1-p) (1/n1+1/n2)

= 0.22-0.41/√0.29(1-0.29)(1/297+1/189)

= -4.49

Critical value at 95% significance level= 1.96( from tables)

We therefore reject null hypothesis as critical value is greater than test statistic

Therefore the sentiment for increasing speed limit in the two populations is different

b. at proportions of 0.24 and 0.40 for p1 and p2 respectively

Test statistic = 0.24-0.40/0.29(1-0.29)(1/297+1/189)

= -3.78

P value is 0.0002 at 0.05 significance level

Hence probability =0.4998

7 0

2 years ago

Find the surface area of the square pyramid. A) 104 cm2 B) 160 cm2 C) 224 cm2 D) 448 cm2

jeyben [28]

Answer:
B
Step-by-step explanation:

i

8 0

1 year ago

sonja wants to have $14000 in 13 years. calculate how much she should invest now at 6% interest, compounded semiannually in orde

mariarad [96]

She should invest $6491.73.

The equation we use to solve this is in the form
$A=p(1+\frac{r}{n})^{nt}$ ,
where A is the total amount in the account, p is the principal invested, r is the interest rate as a decimal, n is the number of times per year the interest is compounded, and t is the amount of time.

A in our problem is 14000.
p is unknown.
r is 6% = 6/100 = 0.06.
n is 2, since it is compounded semiannually.
t is 13.

$14000=p(1+\frac{0.06}{2})^{13*2}
\\
\\14000=p(1+0.03)^{26}
\\
\\14000=p(1.03)^{26}
\\
\\\text{Dividing both sides by }1.03^{26}\text{, we have}
\\
\\\frac{14000}{1.03^{26}}=\frac{p(1.03)^{26}}{1.03^{26}}
\\
\\6491.73\approx p$

5 0

2 years ago

when completed (fill in the bank), the following paragraph proves that AB is congruent to BC making ABC an isosceles triangle

Luda [366]

Given: Base ∠BAC and ∠ACB are congruent.

Prove: ΔABC is an isosceles triangle.

When completed (fill in the blanks), the following paragraph proves that Line segment AB is congruent to Line segment BC making ΔABC an isosceles triangle.

Construct a perpendicular bisector from point B to Line segment AC.

Label the point of intersection between this perpendicular bisector and Line segment AC as point D.

m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector.

∠BDA is congruent to ∠BDC by the definition of congruent angles.

Line segment AD is congruent to Line segment DC by by the definition of a perpendicular bisector.

ΔBAD is congruent to ΔBCD by the _______1________.

Line segment AB is congruent to Line segment BC because _______2________.

Consequently, ΔABC is isosceles by definition of an isosceles triangle.

corresponding parts of congruent triangles are congruent (CPCTC)

the definition of a perpendicular bisector

the definition of congruent angles

the definition of a perpendicular bisector

Angle-Side-Angle (ASA) Postulate

corresponding parts of congruent triangles are congruent (CPCTC)

4 0

2 years ago

Thomas took everyone to lunch and there were 11 people at the table. Everyone’s meal cost the same and the total bill was $115.3

NNADVOKAT [17]

Answer: $10.49

Step-by-step explanation:

Each person's meal cost

115.39 / 11 = 10.49

8 0

2 years ago

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