Find the number of real number solutions for the equation.
x2- 6=0

Answer:

See below.

Step-by-step explanation:

9.

Property of a rhombus:

In a rhombus, the diagonals are perpendicular.

The sum of the measures of the angles of a triangle is 180 deg.

Since the diagonals are perpendicular, the angles formed by the intersection of the diagonals are right angles and measure 90 deg.

m<ABD + m<CAB + 90 = 180

50 + m<CAB + 90 = 180

m<CAB + 140 = 180

(i) m<CAB = 40

The diagonals of a rhombus divide the rhombus into 4 congruent triangles.

Call the point of intersection of the diagonals E.

Triangles CEB and AEB are congruent.

m<BCA = m<DCA = 40

m<BCD = m<BCA + m<DCA = 40 + 40

(ii) m<BCD = 80

m<CDB = m<ADB = 50

m<ADC = m<CDB + m<ADB = 50 + 50

(iii) m<ADC = 100

10.

There are two angles labeled z. One is near point E and one is near point O. One of them probably is x.

Two angles measure 60 and 80. Add them to get 140.

z (near point O) and the 140 deg angle are a linear pair. their measures add to 180 deg.

z + 140 = 180

z = 40 (This is the z near point O.)

z (near point O) and 60 deg add to an interior angle of the parallelogram.

z + 60 = 40 + 60 = 100

The interior angle at vertex O measures 100 deg.

Adjacent interior angles of a parallelogram are supplementary.

100 + y = 180

y = 80

The two angles labeled z are alternate interior angles. Since the sides of a parallelogram are parallel, the two angles labeled z are congruent and measure 40 deg.

z = 40 (This is angle z near point E)

Answer:

  H  70 in³

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

  V = (1/3)Bh

  V = (1/3)(21 in²)(10 in) = 70 in³

The volume of the pyramid is 70 cubic inches.

Answer:

[tex]= 70 {in}^{3}[/tex]

Third answer is correct.

Step-by-step explanation:

[tex]v = \frac{base \: \: \: area \times height}{3} \\ = \frac{21 \times 10}{3} \\ = 70 {in}^{3} [/tex]

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Step-by-step explanation:

work is shown and pictured

Answer:

The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.

Step-by-step explanation:

Given a function y, the average rate of change S of y=f(x) in an interval [tex](x_{s}, x_{f})[/tex] will be given by the following equation:

[tex]S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}[/tex]

In this problem, we have that:

[tex]B(t) = 1000(1.02)^{t}[/tex]

Find the average rate of change in the balance over the interval t = 0 to t = 5.

[tex]B(0) = 1000(1.02)^{0} = 1000[/tex]

[tex]B(5) = 1000(1.02)^{5} = 1104.08[/tex]

Then

[tex]S = \frac{1104.08 - 1000}{5-0} = 20.82[/tex]

The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.

Answer:

(0, 8).

Step-by-step explanation:

The y intercept occurs when  = 0, so we have the equation:

y = -3(0) + 8

y = 0 + 8

y = 8.

The answer is (0, 8).

Answer:

Matt ran 6 miles.

Step-by-step explanation:

Stan ran 4 and 7/10 miles, and this is 1 and 3/10 fewer miles than Matt.

this means that Matt ran the following amount of miles

4 and 7/|0 + 1 and 3/10 miles:

(4 + 1) + (7/10 + 3/10) = 5 + 10/10 = 6 miles.

This would be the correct way to solve this equation.

Answer:

12

Step-by-step explanation:

Answer:

152°

Step-by-step explanation:

Let P be any point on tangent [tex] \overleftrightarrow{YZ} [/tex] and WY is secant or chord of the [tex] \odot J[/tex] .

[tex] \therefore m\angle WYZ + m\angle WYP = 180°\\(Straight \: line \: \angle 's) \\

\therefore 104° + m\angle WYP = 180°\\

\therefore m\angle WYP = 180°- 104° \\

\red{\boxed {\bold {\therefore m\angle WYP = 76°}}} \\[/tex]

NOW, by tangent secant theorem:

[tex] m\angle WYP =\frac{1}{2}\times m(\widehat{WXY}) \\\\

76°=\frac{1}{2}\times m( \widehat{WXY}) \\\\

76°\times 2 =m( \widehat{WXY}) \\

\huge \purple {\boxed {\therefore m(\widehat{WXY}) = 152°}} [/tex]

Answer:

Option (3)

Step-by-step explanation:

From the figure attached,

AB and CD are two chords intersecting at O.

m∠AOD = 37°

m∠AOC + m∠AOD = 180° [Since these angles are supplementary angles]

m∠AOC = 180° - 37°

              = 143°

By the theorem of intersecting chords,

Measure of angle formed is the half of the sum of measures of the arcs intercepted by the angle and vertical angle.

m∠AOC = [tex]\frac{1}{2}(\widehat{AC}+\widehat{BD})[/tex]

143° = [tex]\frac{1}{2}[(x+5)+(x-5)][/tex]

143° = x

Therefore, Option (3) will be the answer.

Answer:

70°

Step-by-step explanation:

Since it's a trapezoid the sum of a and x would be 180°

110° + x = 180°

x = 70°

Answer:

Null hypothesis: H0 = 0.65

Alternative hypothesis: Ha ≠ 0.65

z = 1.172

P value = P(Z≠1.172) = 0.24

Decision we fail to reject the null hypothesis. That is, there is convincing evidence enough to reject the Null hypothesis.

Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 95% confidence interval) ---- reject Null hypothesis

Z score < Z(at 95% confidence interval) ------ accept Null hypothesis

Step-by-step explanation:

Given;

n=80 represent the random sample taken

Null hypothesis: H0 = 0.65

Alternative hypothesis: Ha ≠ 0.65

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 80

po = Null hypothesized value = 0.65

p^ = Observed proportion = 57/80 = 0.7125

Substituting the values we have

z = (0.7125-0.65)/√(0.65(1-0.65)/80)

z = 1.17201807734

z = 1.172

To determine the p value (test statistic) at 0.05 significance level, using a two tailed hypothesis.

P value = P(Z≠1.172) = 0.241197 = 0.24

Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 1.172) which falls within the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.24 which is higher than 0.05. Then we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is valid.

Answer:

[tex]-3 \le h \le 1[/tex].

Step-by-step explanation:

Apply the property of absolute values: if [tex]a \ge 0[/tex], then [tex]|x| \le a \iff -a \le x \le a[/tex]. By this property, [tex]|- 3\, h - 6 | \le 3[/tex] is equivalent to [tex]-3 \le -3\, h - 6\le 3[/tex]. That's the same as saying that [tex]-3\, h - 6 \ge -3[/tex] and [tex]-3\, h - 6 \le 3[/tex].

Add [tex]6[/tex] to both sides of both inequalities:

[tex]-3\, h \ge 3[/tex] and [tex]-3\, h \le 9[/tex].

Divide both sides of both inequalities by [tex](-3)[/tex]. Note that because [tex]-3 < 0[/tex], dividing both sides of an equality by this number will flip the direction of the inequality sign.

Both inequalities are supposed to be true. Combining the two inequalities to obtain:

[tex]-3 \le h \le 1[/tex].

Answer:

Step-by-step explanation:

I remember leaving a top of ten percent (15%)

lets convert 15% into a decimal

15%=0.15

Tip=0.15x, where x is the bill price

Tip=0.15*34

Tip=5.1

So he could get  5$ and 10 cents as a tip

Answer:

4

Step-by-step explanation:

Gradient= [tex] \frac{y1 - y2}{x1 - x2} [/tex]

Gradient of line segment

[tex] = \frac{14 - 6}{10 - 8} \\ = \frac{8}{2} \\ =4[/tex]

Answer:

-8 = x

Step-by-step explanation:

-15 = 2x + 1

-1            - 1            Subtract 1 from both sides

-16 = 2x                 Divide both sides by 2

-8 = x

To make sure this answer is correct, plug it into the equation to see if it works.

-15 = 2(-8) + 1       Multiply

-15 = -16 + 1          Add

-15 = -15

Answer:

A tangent line touches a curve at one point and has the same slope as the curve at that point. A secant line intersects at 2 or more points and has a slope equal to the average rate of change between those points.

Answer:

A Tangent of a circle is found outside of the circle but touching 2 points of the circle on the outside. But a Secant is found inside the circle and it touches 2 points in the circle. A Chord can always be Secant, but a secant can not always be a chord because it may pass through the circle.

Step-by-step explanation:

Simplify the expression.

[tex]\frac{y}{2} +\frac{40}{3}[/tex]

Answer:

9 inches

Step-by-step explanation:

For similar problems like this, divide the area by the given length or width. In this case, your equation would be 54/6 = 9.

The width of the rectangle can be found as 9 inch.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The area and length of rectangle are given as 54 inch² and 6 inches.

Suppose the width of the rectangle be x.

Since, the area of rectangle is given as the product of length and breadth, the following equation can be written as,

6x = 54

⇒ x = 54/6

⇒ x = 9

Hence, the width is given as 9 inch.

To know more about linear equation click on,

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Answer:

Rhombus

Step-by-step explanation:

Answer:

Step-by-step explanation:

rhombus

Answer:

D.

Step-by-step explanation:

Let's solve each choice.

A: 3 divided by 90 is 3/90 and can be simplified to 1/30. So no.

B: 1/5 divided by 6. Recall that when dividing, you multiply the 1st term by the 2nd term's reciprocal. If you do this, you get 1/30. So no.

C: 1/6 divided by 5. Again, multiply 5's reciprocal to 1/6. There you get 1/30. So no.

D: 6 divided by 1/5. Again, multiply 1/5's reciprocal to 6. 1/5's reciprocal is 5. 5*6 = 30. So this is the correct answer.

Answer:

[tex]=13x+5[/tex]

Step-by-step explanation:

[tex]\left(2x+9\right)+\left(11x-4\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=2x+9+11x-4\\\mathrm{Group\:like\:terms}\\=2x+11x+9-4\\\mathrm{Add\:similar\:elements:}\:2x+11x=13x\\=13x+9-4\\\mathrm{Add/Subtract\:the\:numbers:}\:9-4=5\\=13x+5[/tex]

Answer:

-$5.06

Step-by-step explanation:

Given the probability distribution of X where X is the net gain or loss

[tex]\left|\begin{array}{c|c|c}Profit(X)&\$6&-\$8\\P(X)&0.21&0.79\end{array}\right|[/tex]

The expected value of X is defined as follows:

Expected Value of X, [tex]E(X)=\sum_{i=1}^nx_iP(x_i)[/tex]

Therefore, the expected value of the player

E(X)=(6*0.21)+(-8*0.79)

=1.26-6.32

[tex]E(X)=-\$5.06[/tex]

The expected value of each player at the casino is -$5.06.

Answer:

Answer:

She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.

Step-by-step explanation:

To find the experimental probability of an outcome we divide:

The number of trials in which the desired outcome happened by the total number of trials.

In this question:

Experimental probability of winning this game.

She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.

Answer:

Shen has a slower heart rate than Adrian.

Shen’s unit heart rate is 64 beats per minute.

Adrian’s unit heart rate is 72 beats per minute.

Answer:

Endangered species

Step-by-step explanation:

An endangered species is a species that is at risk of extinction due to rapid decrease in their population .Their decrease in population might be due to loss of habitat and genetic variation. The loss of habitat might be due to natural factors like the climate change For example animals like dinosaurs during the cretaceous period that experience rapid change in the climate loss their habitat and went extinct.

Human activity can also influence loss of habitat. Development in housing , agriculture and industry can also threaten the habitats of native organisms. The loss of their habitat might cause sudden extinction of these organisms. They might find it hard to adapt to another environment or even procreate.  

Generally,  endangered species are species that are threatened by extinction. Elephants that are in danger of been wiped out is an endangered species.

Answer:

1) With H1: p ≠ 3/5, the test statistic is z = 0.78

The p value for this case would be given by:

[tex] p_v = 2*P(z>0.78)=0.4354[/tex]

Best option:

A) 0.4354; fail to reject the null hypothesis

2) The test statistic in a left-tailed test is z = -1.83

The p value for this case would be given by:

[tex] p_v = P(z<-1.83)=0.0336[/tex]

Best option:

A) 0.0336; reject the null hypothesis

3) The test statistic in a right-tailed test is z = 0.52.

The p value for this case would be given by:

[tex] p_v = P(z>0.52)=0.3015[/tex]

Best option:

C) 0.3015; fail to reject the null hypothesis

Step-by-step explanation:

The significance level for all the cases is the same [tex]\alpha=0.05[/tex]

Part 1

With H1: p ≠ 3/5, the test statistic is z = 0.78

The p value for this case would be given by:

[tex] p_v = 2*P(z>0.78)=0.4354[/tex]

Best option:

A) 0.4354; fail to reject the null hypothesis

Part 2

The test statistic in a left-tailed test is z = -1.83

The p value for this case would be given by:

[tex] p_v = P(z<-1.83)=0.0336[/tex]

Best option:

A) 0.0336; reject the null hypothesis

Part 3

The test statistic in a right-tailed test is z = 0.52.

The p value for this case would be given by:

[tex] p_v = P(z>0.52)=0.3015[/tex]

Best option:

C) 0.3015; fail to reject the null hypothesis

Answer:

Jake

Step-by-step explanation:

Noah: 11 feet per second

Katie: 423 feet / 33 seconds = 12.82 ft/sec (just divide the feet / seconds)

Jake:

1 mile = 5280 feet

Adam runs 5280ft / 396 seconds = 13.34 ft/sec

Liz:

1 minute = 60 second.

Liz runs 638 feet / 60 seconds = 10.63 ft / sec

From the above results we find that Jake runs the fastest

Answer:

36

Step-by-step explanation:

In circle with center O,

[tex] chord\overline {EF} \cong chord\overline {WV}... (Given) [/tex]

Since, congruent chords are equidistant from the center of the circle.

[tex] \therefore PG = GO\\

\therefore - x +10 = - 3(x+2)\\

\therefore - x + 10 = - 3x - 6\\

\therefore 3x - x = - 6-10\\

\therefore 2x = - 16\\\\

\therefore x = \frac{-16}{2} \\\\

\huge \red {\boxed {\therefore x = - 8}} \\\\

\because \overline {PO} = \overline {PG} + \overline {GO} \\

\therefore \overline {PO} = - x + 10 + \{-3(x + 2)\}\\

\therefore \overline {PO} = - x + 10 - 3x - 6\\

\therefore \overline {PO} = - 4x + 4 \\

\therefore \overline {PO} = - 4\times (-8)+ 4 \\

\therefore \overline {PO} =32+ 4 \\

\huge \orange {\boxed {\therefore \overline {PO} =36}} \\[/tex]

Answer:

Step-by-step explanation:

Given that:

An epidemiologist found five cases of "big toe cancer" in the Yukon Territory.

Therefore, shoe size > 9

1) From the required data given below

                       Case       Control       Total

Yes                2(a)             3(b)            5

No                  3(c)             2(d)            5

Total               5                 5                10

∴ odds ratio = ad/bc

= 4/9

=0.444

2) From the less than 1.0 mean that the odds of cancer among case is lower than the odds of cancer among controls